Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 30 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph's average speeds and velocities in jogging (a) from A to B and (b) from A to C?
Answers
Joseph's average speeds and velocities in jogging from A to B will be 2 m/sec and 2 m/sec and from A to C will be 1.90 m/sec and 0.95 m/sec.
What is the average velocity?The average velocity is the ratio of the total distance traveled to the total time taken by the body. Its unit is m/sec.
From points A to B;
Distance covered,d=300m
Displacement,D=300m
Time taken,t=2 min 30 sec
=(2×60)+30
=150 sec
The average speed is found as;
\(\rm S_{avg} = \frac{d}{t} \\\\ \rm S_{avg} = \frac{300}{150} \\\\ S_{avg} =2 \ m/sec\)
The average velocity is found as;
\(\rm V_{avg} = \frac{D}{t} \\\\ V_{avg} =\frac{300}{150} \\\\ V_{avg} =2 \ m/sec\)
Hence, joseph's average speeds and velocities in jogging from A to B will be 2 m/sec and 2 m/sec.
(b)From points A to C;
Distance covered;
d'=300+100=400m
Displacement
D'=300−100
D'=200m
Time taken;
t;=3 min 30 sec
t'=(3×60)+30
t'=210 sec
The average speed is found as;
\(\rm S_{avg} = \frac{d}{t} \\\\ \rm S_{avg} = \frac{400}{210} \\\\ S_{avg} =1.90 \ m/sec\)
The average velocity is found as;
\(\rm V_{avg} = \frac{D}{t} \\\\ V_{avg} =\frac{200}{210} \\\\ V_{avg} =0.95 \ m/sec\)
Hence, joseph's average speeds and velocities in jogging from A to C will be 1.90 m/sec and 0.95 m/sec.
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Related Questions
plz help me!!! I'm make u the brainlyest!!!! plzzzz helpppp
A Car makes a 75-mile trip South in 1 hour. For the first 30 minutes, it drove 50 mph. For the second 30 minutes, it drove 100 mph. Answer the following questions:
a. Instantaneous Velocity at minute 15:
b. Instantaneous Velocity at minute 45:
c. Average velocity of the entire trip in mph:
Answers
Answer:
B
Explanation:
A 5.00-g lead bullet moving at 400 m/s penetrates a wood block and comes to rest inside the block. If half of its kinetic energy goes into heating the bullet, what is the bullet's change in temperature? The specific heat of lead is 128 J/ (kg*K).
Answers
To solve this problem, we need to use the conservation of energy principle which states that the initial kinetic energy of the bullet must be equal to the final internal energy of the bullet plus the work done on the bullet.
The initial kinetic energy of the bullet can be calculated as:
KE = 0.5 * m * v^2
KE = 0.5 * 0.005 kg * (400 m/s)^2
KE = 200 J
Half of this energy will be used to heat the bullet, so the energy that goes into heating can be calculated as:
Q = 0.5 * KE
Q = 0.5 * 200 J
Q = 100 J
We can use the specific heat formula to calculate the change in temperature:
Q = m * c * ΔT
Where Q is the energy absorbed, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Rearranging the formula, we get:
ΔT = Q / (m * c)
ΔT = 100 J / (0.005 kg * 128 J/(kg*K))
ΔT = 156.25 K
Therefore, the change in temperature of the bullet is 156.25 K.
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) If the volume of an object were doubled while its mass remained the same, its density would
A) be half.
B) double.
C) stay the same.
D) be four times as great.
Answers
Given that the volume of an object is doubled while its mass remains the same, we can analyze its effect on density using the formula:
Density = Mass / Volume
Since the mass remains constant and the volume doubles, the new density can be calculated as follows:
New Density = Mass / (2 * Volume)
Now, let's compare the new density with the original density:
New Density / Original Density = (Mass / (2 * Volume)) / (Mass / Volume)
After simplifying, we get:
New Density / Original Density = 1/2
So, the new density is half of the original density.
Therefore, the correct answer is: A) be half.
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If the volume of an object were doubled while its mass remained the same, its density would: A) be half. Density is calculated as mass divided by volume (density = mass/volume)
The density of an object is defined as its mass per unit volume. Therefore, if the volume of an object were doubled while its mass remained the same, its density would be reduced by half. This is because the mass remains constant while the volume is increased, so the same amount of mass is now spread out over a larger volume, resulting in a lower density. Therefore, the correct answer is A) be half. It is important to note that density is an intensive property, which means that it does not depend on the size or amount of the substance. This means that if we have two objects of the same material with different volumes, their densities will be the same as long as their masses are proportional to their volumes. Furthermore, the concept of density is widely used in science and engineering. It is used to describe the properties of materials, to determine the purity of substances, and to solve problems related to buoyancy and fluid mechanics. Understanding the relationship between mass, volume, and density is essential for many fields of study and practical applications.
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Two stars are in a binary system. One is known to have a mass of 1.00 solar masses. If the system has an orbital period of 400 years, and a semi-major axis of 1.34E+10 km, what is the mass of the other star?
Answers
The mass of the other star in the binary system is approximately 0.541 solar masses.
To find the mass of the other star in the binary system, we can use Kepler's Third Law of Planetary Motion, which can be applied to binary star systems. The law states that the square of the orbital period (\(T\)) is proportional to the cube of the semi-major axis (\(a\)) of the orbit. Mathematically, this can be expressed as\(\(T^2 = \frac{4\pi^2}{G(M_1 + M_2)}a^3\), where \(M_1\) and \(M_2\)\) are the masses of the stars,\(\(G\)\) is the gravitational constant, and other variables have their usual meanings.
Given that one star has a mass of 1.00 solar masses, we can substitute the known values into the equation and solve for\(\(M_2\)\). Rearranging the equation, we have\(\(M_2 = \frac{4\pi^2}{G}(\frac{a^3}{T^2}) - M_1\)\).
Plugging in the values for\(\(a\) (1.34E+10 km) and \(T\) (400 years)\), and using the appropriate unit conversions, we can calculate the mass of the other star,\(\(M_2\\), to be approximately 0.541 solar masses.
Therefore, the mass of the other star in the binary system is approximately 0.541 solar masses.
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What is the area of space around a magnet called?
Answers
Answer:
These acts of attraction and repulsion are called “magnetism”, and the magnetic space around a magnet is called the “magnetic field”
Explanation:
solve the problem. select the choice that indicates the correct answer and the correct number of significant figures for each measurement. 91/2.8
Answers
Some examples of significant figures that can help you better understand them are:
104.1097 contains seven significant digits. This is because all zeros that are on the right of a decimal point and also to the left of a non-zero digit is never significant. 0.00798 contains three significant digitsFurthermore, some extra tips are:
All non-zero numbers are always significant.All zeroes before a non-zero number are insignificant. All zeroes which are simultaneously to the right of the decimal point and at the end of the number are significant.What is a Significant Figure?This refers to the digits that carry meaning contributing to its measurement resolution and each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first non-zero digit.
Hence, we can see that:
All non-zero numbers are always significant.All zeroes before a non-zero number are insignificant. All zeroes which are simultaneously to the right of the decimal point and at the end of the number are significant.Read more about significant figures here:
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At least how many Calories does a mountain climber need in order to climb from sea level to the top of a 5.19 km tall peak assuming the muscles of the climber can convert chemical energy to mechanical energy with an efficiency of 10.0 percent. The total mass of the climber and the equipment is 80.0 kg. (Enter your answer as a number without units.)
Answers
The mountain climber would need at least 1,961 Calories to climb from sea level to the top of the 5.19 km tall peak.
To calculate the minimum Calories required by the mountain climber, we need to consider the work done against gravity during the climb. The work done against gravity is given by the formula:
Work = force x distance
The force can be calculated using the formula:
Force = mass x acceleration due to gravity
The mass of the climber and equipment is given as 80.0 kg. The acceleration due to gravity is approximately 9.8 m/s². Therefore, the force is:
Force = 80.0 kg x 9.8 m/s² = 784 Newtons
The distance is the height of the peak, which is 5.19 km or 5,190 meters.
Next, we need to calculate the work done against gravity:
Work = 784 N x 5,190 m = 4,068,960 Joules
Since the question asks for the energy in Calories, we need to convert the work from Joules to Calories. One calorie is equivalent to 4.184 Joules.
Energy in Calories = Work (Joules) / Conversion factor (Joules per Calorie)
Energy in Calories = 4,068,960 J / 4.184 J/Cal = 973,717.67 Calories
However, we need to consider the efficiency of energy conversion from chemical energy to mechanical energy of the muscles, which is given as 10.0 percent. So, the actual amount of Calories required is:
Actual Calories = Energy in Calories / Efficiency
Actual Calories = 973,717.67 Calories / 0.1 = 1,961,435.34 Calories
Rounded to the nearest whole number, the mountain climber would need at least 1,961 Calories to climb from sea level to the top of the 5.19 km tall peak.
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A professional boxer hits his opponent with a 1250-N horizontal blow that lasts for 0.16 s. a) what is the opponents final speed, in meters per second, if his mass is 102.5 kg and he was at rest when struck near his center of mass? B) now assume that just the opponent’s head, with a mass of 4.64 kg, was hit in this manner. Calculate the final speed of his head, in meters per second, assuming the head does not initially transfer significant momentum to the boxer’s body.
Answers
We know that the impulse if related to the momentum as:
\(I=\Delta p\)and related to the average force and the time of the collision by:
\(I=Ft\)Which means that:
\(Ft=\Delta p\)a)
In this case the force is 1250 N, the time is 0.16 s, the initial velocity is 0 and the mass is 102.5 kg, then we have:
\(\begin{gathered} (1250)(0.16)=(102.5)(v_f-0) \\ v_f=\frac{(1250)(0.16)}{102.5} \\ v_f=1.951219512 \end{gathered}\)Therefore the velocity is 1.951219512 m/s.
b)
In this case the force is 1250 N, the time is 0.16 s, the initial velocity is 0 and the mass is 4.64 kg, then we have:
\(\begin{gathered} (1250)(0.16)=(102.5)(v_f-0) \\ v_f=\frac{(1250)(0.16)}{4.64} \\ v_f=43.10344828 \end{gathered}\)Therefore the velocity is 43.10344828 m/s.
Use the motion map to answer the question, describe the position and velocity of the object based moo the motion map?
Answers
answer:
a discus thrower accelerates a discus from rest to a speed of 25.5 m/s by whirling it through 1.30 rev. assume the discus moves on the arc of a circle 1.01 m in radius. (a) Calculate the final angular speed of the discus.___
rad/s
(b) Determine the magnitude of the angular acceleration of the discus, assuming it to be constant. ___
rad/s2
(c) Calculate the time interval required for the discus to accelerate from rest to 25.6 m/s. ___ s
Answers
(a)the final angular speed of the discus is 25.25 rad/s.
(b) the magnitude of the angular acceleration of the discus is 162.2 rad/s^2.
(c)the time interval required for the discus to accelerate from rest to 25.6 m/s is 0.158 s.
(a) The final angular speed of the discus can be calculated using the equation: v = ωr
where v is the linear speed, ω is the angular speed, and r is the radius of the circle.
At the end of the 1.30 revolutions, the linear speed of the discus is 25.5 m/s, and the radius of the circle is 1.01 m. Therefore, we have:
25.5 m/s = ω × 1.01 m
Solving for ω, we get:
ω = 25.5 m/s / 1.01 m = 25.25 rad/s
Therefore, the final angular speed of the discus is 25.25 rad/s.
(b) The magnitude of the angular acceleration of the discus can be calculated using the equation:
α = (ωf - ωi) / t
where ωi is the initial angular speed (which is zero), ωf is the final angular speed (which we just calculated in part (a)), and t is the time interval during which the acceleration occurs.
The discus is whirled through 1.30 revolutions, which corresponds to an angular displacement of:
θ = 2π × 1.30 = 8.168 radians
The time interval t can be calculated using the formula for angular displacement: θ = ωit + (1/2)αt^2
At the beginning of the motion, the initial angular speed is zero, so the formula simplifies to: θ = (1/2)αt^2
Substituting the values we have:
8.168 rad = (1/2)αt^2
Solving for α, we get:
α = 2θ / t^2
The time interval t can be found from the linear speed of the discus, which we know is 25.5 m/s. The distance traveled by the discus during the 1.30 revolutions is:
d = 2πr × 1.30 = 8.18 m
The time interval t is therefore:
t = d / v = 8.18 m / 25.5 m/s = 0.321 s
Substituting this value into the expression for α, we get:
α = 2θ / t^2 = 2 × 8.168 rad / (0.321 s)^2 = 162.2 rad/s^2
Therefore, the magnitude of the angular acceleration of the discus is 162.2 rad/s^2.
(c) The time interval required for the discus to accelerate from rest to 25.6 m/s can be found using the formula: v = at
where v is the final linear speed, a is the constant linear acceleration, and t is the time interval.
The acceleration of the discus is given by the expression we found in part (b), which is 162.2 rad/s^2. The final linear speed is 25.6 m/s. Therefore, we have:
25.6 m/s = (162.2 rad/s^2) × t
Solving for t, we get:
t = 25.6 m/s / (162.2 rad/s^2) = 0.158 s
Therefore, the time interval required for the discus to accelerate from rest to 25.6 m/s is 0.158 s.
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how many wavelengths thick is a 1/2 mm thumbnail
how many wavelengths thick is 100 micrometer thick hair
Answers
The amount of wavelength of light thick is the thumbnail x/y.
Given:
Wavelength of light= x
Thickness of thumbnail= y
The amount of wavelength thick the thumbnail is x/y
What is wavelength?
Wavelength is the distance between identical points (adjacent peaks) in adjacent cycles of a waveform signal propagated in space or along a wire. In wireless systems, this length is usually given in meters (m), centimeters (cm), or millimeters (mm).To know more about wavelength, click the link given below:
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What happens if we nuke a city?
Answers
Answer:
Those who survived the bomb may become deaf or blind, as well as suffer catastrophic burns and injuries. Even people who were not seriously injured could become trapped within a structure or unable to navigate through the wreckage.
Explanation:
Bryson starts walking to school which is 19km away. He travels 19km there before he realizes he forgot his backpack and then walks home to get it. After picking up his bag, he then heads back to school
Answers
Distance represents the length of the path travelled or the separation between two locations. Let x be the distance he walks before realizing that he has left his backpack at home, then the rest of the journey (19 - x) will be covered after he picks up his backpack and heads back to school.
His total distance is twice the distance from his house to school.
Thus, the equation is:2 × 19 = x + (19 - x) + (19 - x).
Simplifying the above equation gives:38 = 38 - x + x38 = 38.
Thus, x = 0 km.
Hence, Bryson walks 0 km before realizing he forgot his backpack.
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Help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
A (the first one)
Explanation:
Physical science please help me this is confusing and hard I can give more points if needed
Answers
The resistor has a resistance of 47 ohms and a maximum power rating of 0.25 watts.
How calculate power to the resistor?The power dissipated by a resistor is given by the formula:
P = V²/R
where P is the power in Watts, V is the voltage across the resistor in Volts and R is the resistance in Ohms.
In this question,
The resistor has a resistance of 47 ohms.
The power dissipation of the resistor is given by the equation
P = V^2/R,
where V is the voltage across the resistor and R is the resistance of the resistor.
The voltage across the resistor is 10 volts,
so the power dissipation of the resistor is (10^2)/47 = 2.128 watts.
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A _____ is a series of events and activities with no slack time. a. risk path b. foundation path c. baseline path d. critical path.
Answers
The D. critical path is a series of events and activities with no slack time.
It is a path that defines the longest duration required to complete a project. It is significant in the project management methodology as it helps the project manager establish a timeline for the project while also identifying the activities that are most critical to the project's completion. If an activity on the critical path takes longer than anticipated, the whole project will be delayed, and if an activity is completed earlier than expected, then it might not be worth it to continue the project, and the client might not be willing to pay for it.
The critical path analysis allows managers to identify and control the critical factors that can impact a project's success, enabling them to focus on the most important areas and make informed decisions about the project. So the correct answer is D. critical path, is a series of events and activities with no slack time.
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Thirteen resistors are connected across points A and B as shown in the figure. If all the resistors are
accurate to 2 significant figures, what is the equivalent resistance between points A and B?
Answers
The equivalent resistance between points A and B in the diagram is 22 Ω
How do I determine the equivalent resistance?We shall begin by obtaining the equivalent resistance in parallel (i,e the three 6 Ω resistor). Details below:
Resistor 1 (R₁) = 6 ΩResistor 2 (R₂) = 6 ΩResistor 3 (R₃) = 6 ΩEquivalent resistance (Rₜ) = ?1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃
1/Rₜ = 1/6 + 1/6 + 1/6
1/Rₜ = 3/6
1/Rₜ = 1/2
Rₜ = 2 Ω
Finally, we shall determine the equivalent resistance between A and B (i.e series arrangement). Details below:
Resistor 1 (R₁) = Resistor 2 (R₂) = ... = Resistor (R₁₁) = 2 ΩEquivalent resistance (R) =?R = R₁ + R₂ + R₃ + R₄ + R₅ + R₆ + R₇ + R₈ + R₉ + R₁₀ + R₁₁
R = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2
R = 22Ω
Thus, we can conclude that the equivalent resistance is 22 Ω
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Photovoltaic cells _____
the sun's energy.
O multiply
collect
dilute
condense
Answers
Answer:
option b collect
Explanation:
Solar PV cells generate electricity by absorbing sunlight and using that light energy to create an electrical current. There are many photovoltaic cells within a single solar panel, and the current created by all of the cells together adds up to enough electricity to help power your home.
What is the average speed of a runner who completes a 400 m lap in 80 s?
Answers
400 divided by 80 will give you the answer!
is acceleration the slope of a velocity-time graph?
Answers
Answer:
Yes!
Explanation:
The slope of a velocity-time graph is indeed equal to the object's acceleration.
Key Space C2 X1 1F 12V 10W V1 12V Key-A GND Using the time constant T-RC, what is the Capacitance that will allow the light to stay on for 5 seconds? C=T/R= Hint The T will be about 4 time periods for 5 seconds total, so the C value must be divided by 4. 0%
Answers
The Capacitance that will allow the light to stay on for 5 seconds is C = 0.4166666666666667 F.
A time constant is defined as the time it takes for a capacitor to charge to about 63.2 percent of its ultimate charge after a change in voltage is applied to it. A capacitor with a time constant of one second, for example, takes approximately one second to reach 63.2 percent of its ultimate charge when it is charged via a resistor.As per the given data, we have:T = 5 secondsR = 12 ohmsC = ? (Unknown)
So, let's calculate the capacitance that will allow the light to stay on for 5 seconds. The formula for the time constant is given by: T = R * C or C = T / R. Put the given values in the formula, we get: C = T / RC = T / R = 5 / 12C = 0.4166666666666667 F. Since the T value is around 4 time periods for a total of 5 seconds, the C value should be divided by 4.Therefore, the Capacitance that will allow the light to stay on for 5 seconds is C = 0.4166666666666667 F.
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4) Gabo bought three chicken dinners for $6.95 each and one hamburger meal for $5.75. He and three friends decide to divide the cost of the meals equally. How much money does Gabo receive in total from his three friends?
(A) $6.35 (B) $6.65 (C) $19.65 (D) $19.95 (E) $26.60
Answers
Answer: the answer is d $19.95
Explanation:
chicken dinner: 6.95 x 3 = 20.85
burger: 5.75
20.85 + 5.75 = 26.6
26.6 divided by 4 (bc theres 4 ppl and the bill needs to be split equally)
26.6/4= 6.65
and since 3 friends are paying him back u gotta do 6.65 x 3 = 19.95
Why is an object’s mass, rather than its weight, used to indicate the amount of matter it contains?.
Answers
An object's mass, rather than its weight is used to indicate the amount of matter it contains because weight is defined as the amount of force due to an existing field (In most cases, gravitational field) that is experienced by the body. The weight of the same body can be different in different environments it's observed.
However, the mass of the body is the exact measure of the amount of matter contained in a body. Which is constant, regardless of the environment, or conditions the body is observed.
Hence, for real-world calculations and experimentation, the mass of the body is considered to represent the amount of matter it contains rather than its weight.
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If a pump handles a fluid at a temperature 177 C and a pressure of 164 psig with 3.66 m/s at suction nozzle. What is the NPSH (ft) available if the vapor pressure of fluid is 134 psia and specific gravity of fluid is 0.89 at 177 C?
A.80
B.90
C.120
D.105
Answers
The NPSH (ft) available is approximately 120 ft. The correct option is C.
To calculate the Net Positive Suction Head (NPSH) available, we need to use the following formula:
\(NPSH (ft) = \left[\dfrac{(P - Pv)} {(\rho \times g)}\right] - \left\dfrac{V^2} { (2 g)}\)
Where:
P is the absolute pressure at the suction nozzle (psia)Pv is the vapour pressure of the fluid (psia)ρ is the density of the fluid (lb/ft^3)g is the acceleration due to gravity (32.2 \(\dfrac{ft}{s^2}\))V is the velocity of the fluid at the suction nozzle (ft/s)Given:
P = 164 psig (pressure at the suction nozzle)Pv = 134 psia (vapour pressure of the fluid)ρ = specific gravity x ρ(water) (density of the fluid)= 0.89 x 62.4 \(\dfrac{lb}{ft^3}\)(assuming water as the reference fluid)g = 32.2 \(\dfrac{ft}{s^2}\) (acceleration due to gravity)V = 3.66 \(\dfrac{m}{s}\) x 3.28 \(\dfrac{ft}{m}\)Calculating NPSH:
P = 164 psig + 14.7 psia (converting psig to psia)
= 178.7 psia
Calculate the density,
ρ = 0.89 x 62.4
ρ = 55.536 \(\dfrac{lb}{ft^3}\)
The velocity is calculated as,
V = 3.66 x 3.28
V = 12.0288 \(\dfrac{ft}{s}\)
\(NPSH (ft) = \dfrac{(178.7 - 134 ) (55.536 * 32.2 )] - (12.0288) } { (2 \times 32.2 )}\)
\(NPSH (ft) = \dfrac{44.7 (1783.1712)] - (0.1888 ) }{ 64.4 }\)
NPSH (ft) = 120 ft
Therefore, the NPSH (ft) available is approximately 120 ft.
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Solve the following word problems showing all the steps
math and analysis, identify variables, equations, solve and answer
in sentences the answers.
A 30-kg box is dragged to the right across a surface.
horizontal with a net force of 30 N. If the coefficient of kinetic friction
between the ground and the box is 0.35, determine:
a. the friction between the box and the surface
b. the force applied to the box to the box
Answers
Mass of the box, m = 30 kg, Net force acting on the box, F = 30 N, Coefficient of kinetic friction between the box and the ground, μ = 0.35
(a) The friction between the box and the surface. We know that the formula for friction is given as: F = μN, where,F = force of frictionμ = coefficient of friction, N = Normal force acting on the object. Hence, the force of friction acting on the box can be determined by using the above formula.Substitute the given values in the formula:F = μN = μmgWhere g is the acceleration due to gravity and m is the mass of the objectF = (0.35) (30 kg) (9.8 m/s²) = 102.9 N. Therefore, the friction between the box and the surface is 102.9 N.
(b) The force applied to the box. We know that the formula for Newton's second law of motion is: F = ma, Where,F = net force acting on the object, m = mass of the object, a = acceleration of the object. Hence, the force applied to the box can be determined by using the above formula.Substitute the given values in the formula:F = ma = (30 kg) (1 m/s²) = 30 N. Therefore, the force applied to the box is 30 N.
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How does energy in the food chain flow to an omnivore such as a fox?
A) The fox is a plant eater and receives energy directly from plants.
B) The fox receives energy directly from the sun and the plants it eats.
C) When the fox eats an animal that eats plants, it receives energy directly from the sun.
D) When the fox eats an animal that eats plants, it receives energy indirectly from the sun.
Answers
The correct answer is option D) When the fox eats an animal that eats plants, it receives energy indirectly from the sun.
How does energy flow in a food chain?Energy in a food chain flows from the sun, to the producers (plants), to the primary consumers (herbivores), to the secondary consumers (carnivores), and so on. Omnivores, such as foxes, consume both plants and animals, but they typically obtain more of their energy from consuming other animals.
When a fox eats an animal that eats plants, it is receiving energy indirectly from the sun. The plants that the prey animal consumed converted the energy from the sun into organic molecules through the process of photosynthesis. The prey animal then consumed those plants and converted the organic molecules into its own tissues. When the fox eats the prey animal, it is obtaining the energy stored in the prey's tissues.
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A soccer ball is kicked upward from a height of 6 ft with an initial velocity of 96 ft/s. How high will it go? Use -32 ft/s? forthe acceleration caused by gravity. Ignore air resistance.
Answers
Given,
The initial height of the soccer ball, h₁=6 ft
The initial velocity of the ball, u=96 ft/s
The acceleration due to gravity, g=-32 ft/s
When the ball reaches the maximum height, its velocity will reduce to zero.
Thus the velocity of the ball when it is at its maximum height is v=0 ft/s
From the equation of motion,
\(v^2-u^2=2gh_2\)Where h₂ is the total height covered by the ball from its initial height to reach its maximum height.
On substituting the known values,
\(\begin{gathered} 0-96^2=2\times-32\times h_2 \\ \Rightarrow h_2=\frac{-96^2}{2\times-32} \\ =144\text{ ft} \end{gathered}\)Thus the maximum height reached by the ball is,
\(\begin{gathered} H=h_1+h_2 \\ =6+144 \\ =150\text{ ft} \end{gathered}\)Thus the maximum height reached by the ball is 150 ft.
10 rectangular object's mass from greatest to least. You can choose books, sandwiches, phones, pictures - as long as the shape is a rectangle. Then rank the objects from the one with the heaviest mass to the one with the lightest mass.
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Answer: 1 is phone 2 is sandwich, Last is picture.
Explanation: I hoped That Helped !!
a 12.0 meter length of copper wire has a resistance of 1.50 ohms. how long must an aluinum wire with the same cross-sectional area be to hsae the damr resistance
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The length of the nichrome wire that has the same resistance as the 12.0-meter copper wire is approximately \(\( 0.13 \, \text{m} \)\).
To find the length of the nichrome wire that has the same resistance as the 12.0-meter copper wire, we can use the formula for resistance:
\(\[ R = \frac{{\rho \cdot L}}{{A}} \]\)
where \(\( R \)\) is the resistance, \(\( \rho \)\) is the resistivity, \(\( L \)\) is the length of the wire, and \(\( A \)\) is the cross-sectional area.
Given:
Length of the copper wire, \(\( L_c = 12.0 \, \text{m} \)\)
Resistance of the copper wire, \(\( R_c = 1.50 \, \Omega \)\)
Resistivity of copper, \(\( \rho_c = 1.7 \times 10^{-8} \, \Omega \cdot \text{m} \)\)
Resistivity of nichrome, \(\( \rho_n = 1.5 \times 10^{-6} \, \Omega \cdot \text{m} \)\)
Let's calculate the cross-sectional area of the copper wire using the resistance formula:
\(\[ A_c = \frac{{\rho_c \cdot L_c}}{{R_c}} \]\\\\\ A_c = \frac{{1.7 \times 10^{-8} \cdot 12.0}}{{1.50}} \\\\= 1.36 \times 10^{-7} \, \text{m}^2 \]\)
Next, we can use the resistance formula to find the length of the nichrome wire:
\(\[ R_n = \frac{{\rho_n \cdot L_n}}{{A_c}} \]\)
We need to solve for \(\( L_n \)\):
\(\[ L_n = \frac{{R_n \cdot A_c}}{{\rho_n}} \]\)
Substituting the given values:
\(\[ L_n = \frac{{1.50 \cdot 1.36 \times 10^{-7}}}{{1.5 \times 10^{-6}}} \\\\= 0.13 \, \text{m} \]\)
Therefore, the length of the nichrome wire that has the same resistance as the 12.0-meter copper wire is approximately \(\( 0.13 \, \text{m} \)\).
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if the rank of a is r, then occurs as an eigenvalue of a with multiplicity r.
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If λ occurs as an eigenvalue of A with multiplicity r, then there are r linearly independent eigenvectors associated with λ, and the geometric multiplicity of λ is equal to r.
Let A be an n × n matrix. An eigenvalue of A is a scalar λ such that there is a nonzero vector x satisfying the equation Ax = λx. This equation can be rewritten as the linear system (A − λI)x = 0, where I is the identity matrix. Nontrivial solutions to this equation exist if and only if the matrix A − λI is singular, which means that its determinant is zero. Thus, the eigenvalues of A are the roots of the polynomial equation det(A − λI) = 0, which is called the characteristic equation of A. The algebraic multiplicity of an eigenvalue is the number of times it appears as a root of the characteristic equation. The geometric multiplicity of an eigenvalue is the dimension of the eigenspace associated with that eigenvalue. The eigenspace of an eigenvalue λ is the set of all eigenvectors of A associated with λ, along with the zero vector.
The rank of A is the dimension of its column space, which is the span of its column vectors. The rank of A is equal to the dimension of the row space of A, which is the span of its row vectors. The rank of A is also equal to the number of nonzero singular values of A. If the rank of A is r, then the dimension of the nullspace of A is n − r. If A has r linearly independent eigenvectors associated with a particular eigenvalue λ, then the geometric multiplicity of λ is r. If the algebraic multiplicity of λ is greater than its geometric multiplicity, then there are not enough eigenvectors to form a basis of the eigenspace associated with λ, which means that A is not diagonalizable. If the algebraic multiplicity of λ is equal to its geometric multiplicity, then A is diagonalizable. If λ occurs as an eigenvalue of A with multiplicity r, then there are r linearly independent eigenvectors associated with λ, and the geometric multiplicity of λ is equal to r.
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