a) The efficiency of the engine is 67% b) The energy expelled to the cold reservoir in each cycle is 307.89 J
Qh=330 J , W= 22.0 J
a) n= W/Qh = 22 J/330 J = 0.06675 = 0.067
b) n= W/Qh = (Qh-QL)/Qh = 1 - QL/Qh
Plugging values,
0.067 = 1 - QL/330 => QL = 307.89 J
As a ratio of useful work completed to heat produced, an engine efficiency is determined. completed the task. The power delivered at the clutch or the driveshaft is referred to as the "work done" in this context. As a result, the work produced by thermodynamic expansion is reduced by losses such as friction and other losses. Today's gasoline engines are only about 30 to 35 percent efficient, meaning that about 65 cents of every dollar you spend on gas is wasted even with routine auto maintenance like a tune-up or an oil change. According to the Second rule of thermodynamics, it is impossible for heat engines to achieve 100% thermal efficiency.
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A rock is thrown straight upward, reaching a height of
20 meters. On its way up, does the rock spend more time in
the top 5 meters of its flight than in the first 5 meters of its
flight? Explain.
The rock takes more time in second 5m of its journey than it does in the first 5 when thrown straight upward.
Define the term Free Fall?The downward motion that merely acts as a result of gravity is referred to as free fall. In the absence of air, all things in free fall accelerate the same regardless of mass since its acceleration is equal to a acceleration caused by gravity.
The height of fall h = 20 meters.
If we suppose that a rock takes t1 seconds to move the first 5 meters, we may compute the rock's initial speed as follows:
u = √2gh
u = √2*9.81*20
u = 19.80 m/s
The 3rd kinematic motion equation yields the following results:
v² = u² - 2g(hf - hi)
v = √(19.80² - 2*9.81*5)
v = 17.14 m/s
Using the first motion equation we can determine how long it will take the rock to move the first 5m, and we get:
t1 = (u - v) / g
t1 = (19.80 - 17.14)/9.81
t1 = 0.27 s
Similar to this, if a rock takes t2 to move 5 meters, then
v'² = u² - 2g(hf - hi)
v' = √(19.80² - 2*9.81*(20 - 5))
v' = 9.88 m /s
Using the first equation for motion, we can determine how long it will take the rock to move the last 5 m, and we get:
t2 = (v' - u')/g
t2 = (9.88 - 0)/9.81
t2 = 1.00 s
Thus, t2 > t1
As a result, the rock takes more time in the second 5m of its journey than it does in the first 5.
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4. Name three things that all games, no matter where they are played around the world, have in common.
Answer:
Key components of games are goals, rules, challenge, and interaction.
Explanation:
Hope I helped.
Answer:
the name of the games are goals, rules, challenges and interaction and mabe there can be more.
Explanation:
I hope this helped your day better this is the correct answer i got it correct on the test.
Which is the pathway for information through a neuron?
dendrite → axon → cell body → axon terminals
axon terminals → axon → cell body → dendrite
dendrite → cell body → axon → axon terminalsWhich structures produce a fluid to protect the body in the first line of defense? Select four options.
hair
stomach
mouth
eyes
skin
cell body → dendrite → axon → axon terminals
Answer:
cell body → dendrite → axon → axon terminals
Explanation:
im in edgunity
a thermistor is a temperature sensor that contains metallic wire that changes its electrical resistance when the temperature changes
A thermistor is a type of temperature sensor that uses metallic wire to modify its electrical resistance in response to variations in temperature. Temperature can be used to define a metal's resistance.
What are the different varieties of thermistors?The resistance of thermistors is significantly more temperature-dependent than that of conventional resistors. The words thermal and resistor are combined to form the word thermistor. The conduction model used to classify thermistors.
Why are thermistors used?A thermistor's basic task is to gauge a device's internal temperature. The thermocouple is a minor but crucial component of a bigger system in a temperature-controlled system. The thermistor's temperature is kept under observation by a controller.
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• Develop an explanation to demonstrate how frequency, wavelength, and infrared light are all
related to each other.
• Using this explanation, describe why each animal image is different from the other.
Answer:
The higher the frequency, the shorter the wavelength. Because all light waves move through a vacuum at the same speed, the number of wave crests passing by a given point in one second depends on the wavelength.
Explanation:
just as wavelength and frequency are related to light, they are also related to energy. The shorter the wavelengths and higher the frequency corresponds with greater energy. So the longer the wavelengths and lower the frequency results in lower energy. The energy equation is E = hν.
Which of the following accurately describes the behavior of water when subjected to temperature change? Question 9 options: A) The volume of water will decrease if heated from 6°C to 7°C. B) The volume of water will increase if cooled from 3°C to 2°C. C) A mass of water will contract if cooled from 1°C to 0°C. D) A mass of water will expand if heated from 0°C to 2°C.
The behavior of water when subjected to temperature change is that the volume of water will increase if cooled from 3° to 2°C.
The chemical compound water, which can exist in the gaseous, liquid, and solid phases, is made up of the elements hydrogen and oxygen in the ratio 2: 1 i.e. 2 atoms of hydrogen and 1 atom of oxygen.
In general
Volume of water depends on the temperature and is directly proportional to it.
Thus, as the temperature rises, the molecules of water gain energy and move more quickly, which causes the molecules to spread apart and increase the volume of the liquid.
When water cools, it initially contracts (decreases in volume) until a temperature of about four degrees Celsius (4°C).
But at temperatures below 4.0° C, water undergoes an abnormal expansion that causes its volume to start to rise.
This ability is related to the formation of hexagonal structures, which take up a lot of room and increase the volume of the water, as a result of strong hydrogen bonding between water molecules at a lower temperature.
Hence, the volume of water will increase if cooled from 3° to 2°C
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What is mass? Write two differences between fundament .
Mass is a measure of the amount of matter in an object and is a fundamental property of matter. Fundamental forces refer to the interactions between particles, whereas fundamental particles are the building blocks of matter.
Mass is a measure of the amount of matter in an object, usually measured in kilograms (kg). It is a fundamental property of matter that does not change with location or gravitational forces.
Two differences between fundamental forces and fundamental particles are:
1. Fundamental forces refer to the interactions between particles, whereas fundamental particles are the building blocks of matter that makeup everything in the universe.
2. There are four fundamental forces - gravitational, electromagnetic, weak nuclear, and strong nuclear - while there are six types of fundamental particles - quarks, leptons, bosons, neutrinos, antimatter particles, and Higgs bosons.
Therefore,A fundamental characteristic of matter is mass, which is a measurement of how much matter there is in an item. Fundamental particles are the building components of matter, whereas fundamental forces relate to the interactions between particles.
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If we ignore air resistance, a falling body will fall 16t2 feet in t seconds. What is the average velocity between t
Answer:
262.4 m/s
Explanation:
The complete question is
If we ignore air resistance, a falling body will fall 16t^2 feet in t seconds. What is the average velocity between t=8 and t=8.4? Round your answer to two decimal places if necessary.
The distance fallen s = 16t^2
The velocity v = \(\frac{ds}{dt}\) = 32t
If we substitute the values of t into the velocity v, we'll have
at t = 8 s, V1 = 32 x 8 = 256 m/s
at t = 8.4 s, V2 = 32 x 8.4 = 268.8 m/s
Average velocity = (V2 - V1)/2 = (268.8 + 256)/2 = 262.4 m/s
To perform a drug lookup to ensure that the new compound has been added to the computer system properly , select in the toolbar at the top of the screen . a ) Data b ) Close c ) New d ) Save
To perform a drug lookup to ensure that the new compound has been added to the computer system properly we have to select the new from the toolbar at the top of the screen
What is a computer system?A computer system is a collection of computers, related hardware, and related software. The central processing unit (CPU), memory, input/output, and storage devices are the four main components of a computer system. To produce the desired result, all of these parts operate in concert as a single unit.
Selecting the new from the toolbar at the top of the screen will allow us to run a drug lookup to make sure the new compound has been properly added to the computer system.
Therefore the correct answer is the option C
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what is the average velocity if the initial velocity of the object is 10 m/s and the finial velocity is 28 m/s
Answer:
19m/s
Hope this answer is right!!
Explanation:
The initial and final velocity is given and the average velocity is asked, which can be calculated by the following method,
Given that initial velocity = 10 m/s and final velocity = 28 m/s
Average velocity = final velocity+initial velocity/2
Although, average Velocity=total displacement/total time
But here, there is only given initial and final velocity therefore it will be simply an average of the two.
Therefore, the average velocity of the object is 19 m/s.
A 10 kg monkey swings on a vine from a point which is 40 m above the junglefloor to a point which is 15 m above the floor. If the monkey was moving at 2 m/sinitially, what will be his speed at the 15 m point?
In order to determine the final speed of the monkey, use the following equatio, for the final speed in a free fall motion:
\(v^2=v^2_o+2gy\)where,
vo: initial speed = 2m/s
g: gravitational acceleration constant = 9.8m/s^2
y: vertical distance traveled = 40m - 15m = 25m
Replace the previous values of the parameters into the formula for v^2, and apply square root:
\(\begin{gathered} v^2=(2\frac{m}{s})^2+2(9.8\frac{m}{s^2})(25m) \\ v^2=494\frac{m^2}{s^2} \\ v=\sqrt[]{494\frac{m^2}{s^2}} \\ v\approx22.23\frac{m}{s} \end{gathered}\)Hence, at the 15 m point the monkey will have a speed of approximately 22.23m/s
A submarine dove hundreds of feet from the surface of the ocean toward the oceans floor what is the potential energy stored
Potential energy is a form of accumulated energy that an item or set of objects may have depending on their size, shape, location, or even substance.
What is a simple definition of potential energy?Potential energy is the energy retained by an object as a result of its location relative to other objects, internal stresses, electric charge, or other variables. Although it has ties to the old Greek philosopher Aristotle's idea of potentiality, the word potential energy was coined by the 19th-century Scottish engineer and physicist William Rankine.
The gravitational potential energy of an object, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field are all examples of common kinds of potential energy.
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an ideal gas at 20centigree In a press 1.5×10pa and compress,a.isothamally,b.adaibatically until it volume in 1/3 in each case reversible.calculate in each case the final pressure and temperature of d gas (the ratio all specific capacity=Cp/Cv=1.4
a) The final pressure and temperature for the isothermal compression are \(4.5*10^5 Pa\) and 293 K, respectively, while b) the final pressure and temperature for the adiabatic compression are\(5.58*10^5 Pa\) and 515 K, respectively.
a. Isothermal compression:
For an isothermal process, the temperature remains constant. Therefore, we can use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.
Since the process is isothermal, we can write:
\(P_1V_1 = P_2V_2\)
where P1 and V1 are the initial pressure and volume, and\(P_2\)and\(V_2\)are the final pressure and volume.
We are given that the volume is compressed to 1/3 of its original volume, so\(V_2 = (1/3)V_1\). Substituting this into the equation above gives:
\(P_2 = (V_1/V_2)P_1 = 3P_1\) = \(4.5*10^5 Pa\)
To find the final temperature, we can use the ideal gas law again:
PV = nRT
Rearranging, we get:
T = PV/(nR)
Substituting the values we know, we get:
T = (\(1.5*10^5\)Pa)(V1)/(nR)
Since the process is isothermal, the temperature remains constant, so the final temperature is the same as the initial temperature:
T2 = T1 = 293 K
b. Adiabatic compression:
For an adiabatic process, there is no heat transfer between the gas and its surroundings. Therefore, we can use the adiabatic equation:
PV^γ = constant
where γ = Cp/Cv is the ratio of specific heats.
Since the process is adiabatic and reversible, we can write:
\(P_1V_1\)^γ = \(P_2V_2\)^γ
We are given that the volume is compressed to 1/3 of its original volume, so V2 = (1/3)V1. Substituting this into the equation above gives:
\(P_2 = P_1(V_1/V_2)\)^γ = \(P_1\)\((3)^{(1.4)\) = \(5.58*10^5 Pa\)
To find the final temperature, we can use the adiabatic equation again:
\(T_2 = T_1(P_2/P_1)\)^((γ-1)/γ) = T1(5.58/1.5)^(0.4) = 515 K
Therefore, the final pressure and temperature for the isothermal compression are \(4.5*10^5 Pa\)and 293 K, respectively, while the final pressure and temperature for the adiabatic compression are \(5.58*10^5\) Pa and 515 K, respectively.
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A sinusoidal wave travels along a string. The time for a particular point to move from maximum displacement to zero is 0.17 s. What are the (a) period and (b) frequency? (c) The wavelength is 1.5 m; what is the wave speed?
Answer:
31
Explanation:
A point object moves from point A to point B along a circular path with a radius. What is the size of the angle ?
The size of the angle θ of a point object moving from point A to point B along a circular path is 2πR / L.
How to solve size of an angle?To understand this, consider a simple example. Suppose that a point object that moves from point A to point B along a circular path with a radius of 1 meter. The distance between points A and B is also 1 meter. Therefore, the size of the angle θ is equal to 2π × 1 / 1 = 2π radians.
In general, the size of the angle θ = ratio of the circumference of the circle to the distance between points A and B. The circumference of the circle is equal to 2πR, where R = radius of the circle. Therefore, the size of the angle θ is equal to 2πR / L.
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Complete question:
A point object moves from point A to point B along a circular path with a radius R. What is the size of the angle θ?
A voltmeter reading of a circuit it was 6v. The resistance of the bulb was 3 ohms
I. What will be the reading of the ammeter
II. 5 ohm resistor is then added in series what is the reading of the ammeter now
III. If the 5 ohm resistor was added in parallel to the ammeter.
2. Three resistance of 1ohm,3ohm and 4ohm respectively are connected in series to a 12v battery of negligible internal resistance
Calculate the current flowing through each resistor
Explanation:
I. Ohm's law:
V = IR
6 v = I (3 Ω)
I = 2 A
II. Resistors in series:
R = R₁ + R₂
R = 3 Ω + 5 Ω
R = 8 Ω
V = IR
6 v = I (8 Ω)
I = 0.75 A
III. Resistors in parallel:
1/R = 1/R₁ + 1/R₂
1/R = 1 / (3 Ω) + 1 / (5 Ω)
R = 1.875 Ω
V = IR
6 v = I (1.875 Ω)
I = 3.2 A
2. Resistors in series:
R = R₁ + R₂ + R₃
R = 1 Ω + 3 Ω + 4 Ω
R = 8 Ω
V = IR
12 v = I (8 Ω)
I = 1.5 A
An object is projected horizontally at 14.1 m/s from the top of a 195.0 meter cliff.
How far from the base of the cliff will the object strike the ground?
What does a physical map show?
the names of countries, states, and cities
the history of an area
the geographical features of an area
the rest stops and restaurants in an area
Using the periodic table, determine which of the following atoms is most likely to form a positive ion?
Using the periodic table Calcium (Ca) is most likely to form a positive ion.
What is ion?Ion is a type of particle that has an electric charge. It can be positively or negatively charged, depending on its atomic structure and the number of protons and electrons it contains. Positively charged ions are called cations and negatively charged ions are called anions. Ions play an important role in a variety of physical and chemical processes, such as forming ionic bonds, allowing substances to dissolve in water, and carrying electrical current in solutions. They are also important in the formation and stability of molecules, as well as in the formation of compounds and minerals.
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Pls give me the answer asap
Raju's statement is not correct fully as it states that uniform motion is seen only in objects traveling in a straight line while ,Tejas is correct in pointing out that uniform motion can also be observed in objects traveling in circular motion.
Uniform motion refers to the movement of an object at a constant speed in a particular direction. In this type of motion, the object covers equal distances in equal intervals of time. Suppose for example (straight line movement), a car moving on a straight road at a constant speed of 60 km/h. If the car maintains this speed without any change in direction, it exhibits uniform motion. Other example is regarding the object moving in circular path where a race car driving around a circular track with a radius of 100 meters. If the car maintains a constant speed of 40 meters per second and completes each lap in the same amount of time, it exhibits uniform motion. Therefore, Tejas' justification is valid, as he states that uniform motion can indeed be observed in objects traveling in circular paths, in addition to objects moving in straight lines.
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if a bus drives 2km due east,5km 45 degrees north of east, 4km at 30 degrees north of west, then 2km due south. what is the bus's resultant displacement?
The bus resultant displacement is approximately 4.14 km at an angle of 59.5 degrees north of east.
The first movement is 2 km due east, which means it has an x-component of 2 km and a y-component of 0 km.
The second movement is 5 km at 45 degrees north of east. This can be broken down into x and y components using trigonometry: x = 5 km * cos(45) = 3.54 km y = 5 km * sin(45) = 3.54 km
The third movement is 4 km at 30 degrees north of west. This can also be broken down into x and y components using trigonometry: x = -4 km * cos(30) = -3.46 km (negative because it’s towards the west) y = 4 km * sin(30) = 2 km
The fourth movement is 2 km due south, which means it has an x-component of 0 km and a y-component of -2 km.
Adding up all the x and y components, we get: x_total = 2 + 3.54 + (-3.46) + 0 = 2.08 km y_total = 0 + 3.54 + 2 + (-2) = 3.54 km
The magnitude of the resultant displacement can be calculated using the Pythagorean theorem: resultant_displacement = sqrt(x_total^2 + y_total^2) = sqrt(2.08^2 + 3.54^2) ≈ 4.14 km
The direction of the resultant displacement can be calculated using the arctan function: direction = arctan(y_total / x_total) ≈ 59.5 degrees north of east
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a) Write a selected signal assignment statement to represent the 4-to-1 MUX shown below. Assume that there is an inherent delay in the MUX that causes the change in output to occur 15 ns after a change in input.
(b) Repeat (a) using a conditional signal assignment statement.
Selected signal assignment statement to represent the 4-to-1 MUX has been shown below.
a)entity mux4to1 is
port(A,B: in std_logic;
CD : in std_logic_vector(1 down to 0),
F: out std_logic);
end mux4to1;
Architecture behavioral of mux4to1 is
begin
with CD select
F<= transport (not A) after 10 ns when "00",
transport B after 10 ns when "01",
transport (not B) after 10 ns when "10",
transport "0" after 10 when "11";
end behavioral;
b)entity mux4to1 is
port(A,B: in std_logic;
CD : in std_logic_vector(1 down to 0),
F: out std_logic);
end mux4to1;
Architecture behavioral of mux4to1 is
begin
F <= inertial (not A) after 10 ns WHEN (CD = “00”) ELSE
inertail B after 10 ns WHEN (sel = “01”) ELSE
inertail (not B) after 10 ns WHEN (sel = “10”) ELSE
inertail "0" after 10 ns WHEN (sel = “11”) ELSE
‘X’;
end behavioral;
c)entity mux4to1 is
port(A,B: in std_logic;
CD : in std_logic_vector(1 down to 0),
F: out std_logic);
end mux4to1;
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Four cuboids are shown in the diagram below. The position of their center of mass is also shown. Which of the cuboids is the most stable.
The position of their center of mass is also shown. the square cuboids is the most stable. Hence option B is correct.
A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces. Cuboid is short for "like a cube". A cuboid is similar to a cube in that a cuboid may become a cube by varying the lengths of the edges or the angles between the faces.
The square cuboid has its center of mass on the center of square, the masses are uniformly distributed about it.
Hence option B is correct.
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An elephant of mass 2800kg has feet of average area of 200 cm2. A vulture of mass 12 kg walks beside the elephant on a muddy area, the average area of the feet of the vulture is 2.0 cm2. Which one is likely to sink? Explain your answer showing any necessary calculations.
Explanation:
The formula we are going to use is
Pressure = F/A
Elephant:
First, we need to convert weight into newtons.
1kg=9.8 newtons, so 2800kg × newtons = 27440newtons
For 4 feet= 200×4= 800cm^2
Convert the area to meter squared using the following:
1 centimeter squared = 0.0001 meters squared
800cm^2×0.0001= 0.08m^2
Pressure=F/A
Pressure= 27440/0.08
The pressure exerted on the ground by the elephant is 343000 Pascals.
Vulture:
12kg×9.8=117.6newtons
for 2 feet= 2.0×2=4cm^2
4×0.0001=0.0004m^2
117.6/0.0004= 294000 Pascals
To compare the pressure, just do a ratio of the elephant's pressure to vulture's pressure.
343000/294000≈ 1.17
So the pressure is about 1 times bigger.
Keep in mind that the elephant has 4 feet, which help to increase the area which in turn decrease the pressure.
Elephant's feet are more likely to sink as elephant's feet apply more pressure on the muddy area.
What is pressure?Pressure is defined as the thrust per unit area. Thrust is the perpendicular force applied. Its SI unit is pascals.
So, P = T/A
Here,
Mass of elephant = 2800 kg
Force applied = 2800 × 9.8 ( 1kg = 9.8 N)
= 27440 N
Average feet area of elephant = 200 cm2
Since an elephant has 4 feet,
200 × 4 = 800 cm2 = 0.08 m2
Now, P = F/A
27440/0.08 = 343000 pascals
For the vulture,
Force of the vulture = 12 × 9.8 = 117.6 N
Area = 2.0 × 2 = 4cm2 = 0.0004 m2
Now, P = 117.6 / 0.0004 = 294000 pascals
So, pressure applied by the elephant's feet is more than the pressure applied by the vulture's feet. Therefore, the elephant's feet will sink.
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7. Imagine you could look at the flashlight from behind your object, looking
from the darkest and lightest parts of the object's shadow. How much of
the light source do you think you could see from each location?
From the darkest part of the object's shadow, you would be able to see a small amount of the light source. There would be a small amount of light that is visible, but it would be faint. On the other hand, from the lightest part of the shadow, you would be able to see much more of the light source. The light source would be far brighter and more visible, and you would be able to identify the source of the light.
Hope this helps! Have a nice day. :)Explain the Newton's formula for the velocity of sound in air and raplace correction ?
Explanation:


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Question

State Newton's formula for the velocity of sound in a gas. What is the Laplace's correction?
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Updated on : 2022-09-05
Solution

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According to Newton, velocity of sound in any medium is given by v=pE where E is the modulus of elasticity and p is the density of the medium.
For gases E = B, bulk modulus
∴v=pB.............(1)
When sound waves travel through a gas alternate compressions and rarefactions are produced. At the compression region pressure increases and volume decreases and at the rerefaction region pressure decreases and volume increases. Newton assumed that these changes take place under isothermal conditions i.e., at a constant temperature.
Under isothermal condition, B = P, pressure of the gas.
∴ In (1) v=pP.............(2)
This is Newton's formula for velocity of sound in gas.
For air at NTP, P=101.3 kPa and p=1.293 kgm−3
Substituting the values of P and p in, equation (1) we get v = 280 m/s. This is much lower than the experimental value of 332 m/s. Thus Newton's formula is discarded.Laplace's correction:
According to Laplace, in a compressed region temperature increases and in a rarefied region it decreases and these changes take place rapidly. Since air is an insulator, there is no conduction of heat. Thus changes are not isothermal but adiabatic.
Under adiabatic condition, B=y P, where y is the ratio of specific heats of the gas.
Substituting in equation (1) v=pγP
The above equation is called Newton - Laplace's equation
Sunstituting the values of P, p and y in the above equation, give the velocity of sound in air at NTP to be about 331 m/s. This is in close agreement with the experimental value.
Part F
Imagine you were a sportscaster at the Olympics. You'd created a mathematical model similar to the one you just did. Imagine that you had a
computer program that could do an instantaneous analysis of video motion using that model. How could you use it in your sportscast?
A program that could do an instantaneous analysis of video motion will be useful it in a sportscast to analyze events as they occur.
Why will a program be needed?A motion video is defined as the display of video images at a rate (such as thirty frames per second) that causes objects to appear to move smoothly and continuously.
Sports inherently involve fast and accurate motion, which can be difficult for competitors to master but also for coaches and trainers to analyze and audiences to follow. Because of the nature of most sports, monitoring with sensors or other devices attached to players or equipment is generally not possible. This opens up a plethora of opportunities for the use of computer vision techniques to assist competitors, coaches, and the audience
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How much work done when .0080 C is moved through a potential difference of 1.5 V? Use W = qV. A.
Answer:
0.012 J
Explanation:
We are given:
q = 0.0080C
Potential difference = 1.5V
W=qV
Substituting the values into the equation:
W=0.0080*1.5= 0.012J
A concave mirror has a radius of curvature of 1.6m. Find the focal length
Answer:
given,
Radius of curvature of concave mirror = 1.6m
We know that ,
Focal length = radius/2
Hence ,
Focal length of concave mirror = radius of concave mirror /2
=> F = 1.6/2
=> F = 0.8m
Hence the focal length of concave mirror is 0.8 m
Explanation:
Find the first few terms of the Maclaurin series for each of the following functions and check your results by computer.
1/ 1+x+x^2
The first few terms of the Maclaurin series for each of the following functions f(x) = 1 + x + 2x² + 3x³ + 5x⁴ + 8x⁵ + ...
To find the Maclaurin series for the function f(x) = 1/(1+x+x² ), we can use the formula for the geometric series:
1/(1-r) = 1 + r + r² + r³ + ...
If we let r = x + x² , then we have:
f(x) = 1/(1+x+x² ) = 1/(1 - (x+x² ))
Using the formula for the geometric series, we can expand this as:
f(x) = 1 + (x+x² ) + (x+x² )² + (x+x² )³ + ...
Expanding the terms, we have:
f(x) = 1 + x + 2x² + 3x³ + 5x⁴ + 8x⁵ + ...
We can check our answer using a computer program, such as Python.
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Two objects travel the same distance. The one that is moving faster will:
Take more time to go the distance
Take less time to go the same distance
Take the same time as the slower object
None of the above
Answer: take less time to go the same distance
Explanation:
Because if it is going faster let’s say mph 60 mph is 60 miles per hour if you are going 40 miles per hour it will take you longer to get to your destination.