Consider a weather balloon floating in the air. There are three forces acting on this balloon: the force of gravity is FG, the force from lift towards balloon is FL, and the force from the wind is labeled Fw. The orientation of these forces along with a coordinate system is given below:

Assume that || FG || = 20 N, || FL ||= 25 N, and || Fw ll = 15 N.

Required:
Find the magnitude of the resultant force acting on the weather balloon and round your answer to two decimal places.

Answers

Answer 1
Hey I just got home from work

Related Questions

A small car of mass 500 kg is pushing a large truck of mass 980 kg due east on a level road. The car exerts a horizontal force of 1500 N on the truck. What is the magnitude of the force that the truck exerts on the car

Answers

Answer:

Below

Explanation:

Equal and opposite 1500 N

compare the frequency of an electromagnetic wave with the frequency of the vubrating charge that produces the wave

Answers

An electromagnetic wave's frequency is the same as the frequency of the vibrating charge that causes it. The amount of vibrations, or back and forth motions, that occur in a charge in a second, is known as its frequency.

What is meant by electromagnetic waves?

Electromagnetic waves, often known as EM waves, are waves that are produced when an electric field and a magnetic field vibrate together. In other words, the oscillation of the magnetic and electric fields results in electromagnetic (EM) waves. In contrast to mechanical waves, electromagnetic waves can move through voids. This suggests that electromagnetic waves can travel into empty space in addition to through solid materials like air and rock.

What is the significance of electromagnetic?

Food-borne microorganisms can be eliminated by the widespread use of electromagnetic radiation in food preparation. Recent research on the microwave or radio wave portion of the electromagnetic spectrum has found promising results for the inactivation of germs in food preparation.

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What is the equation used to find the angle of refraction? Identify each variable. (1 point)

Answers

Answer:

pictures please

Explanation:

I need a picture so I can tell you

Ferdinand the frog is hopping from lily pad to lily pad in search of a good fly
for lunch. If the lily pads are spaced 2.4 m apart, and Ferdinand jumps with a
speed of 5.4m/s, taking 0.60 s to go from lily pad to lily pad, at what angle
must Ferdinand make each of his jumps?

Answers

Answer:

θ = 33°

Explanation:

Here, we can use the formula for the total time of flight of a projectile to calculate the launch angle of frog:

\(T = \frac{2\ u\ Sin\theta}{g} \\\\Sin\theta = \frac{Tg}{2u}\)

where,

θ = launch angle = ?

T = Total time of flight = 0.6 s

g = acceleration due to gravity = 9.81 m/s²

u = launch speed = 5.4 m/s

Therefore,

\(Sin\theta = \frac{(0.6\ s)(9.81\ m/s^2)}{(2)(5.4\ m/s)}\\\\\theta = Sin^{-1}(0.545)\)

θ = 33°

I don’t get it pls help

I dont get it pls help

Answers

Answer:

Explanation:

Neither do we. It's just a disconnected statement devoid of any context.

From English studies, an "an" leading the phrase means the following word starts with a vowel.

If the object is moving with varying speed, then the blank could be filled with

"unbalanced"

or

"accelerating"

If the object is dropping, then the blank could be filled with a frictional air resistance acting

"upward"

If the object is wiggling, try

"alternating"

If the object is flying, try

"aerodynamic"

I'm sure I could think of others , but it seems a waste of time guessing.

The speed of x-rays is 300 000. m/s. In scientific notation, and with the correct number of significant figures, this speed is… *

Answers

Answer:

3.0 x 10 and the exponent on ten is 5.

Explanation:

You are moving the decimal point over to the left 5 times, making the exponent a positive 5 and then you would put a decimal after 3. Making it 3.0 x 10, and the exponent 5.

The speed of x-rays in scientific notation is 3.0 x 10⁶ m/s.

The given parameters;

speed of the x-ray, v = 300,000 m/s

The standard form of the given number represents the scientific notation of the number.

To represent a number in standard form, multiply the number in terms of power or exponent of 10. The value of the exponent represents the number of available zeros present.

In scientific notation the speed of the x-ray can be expressed as follows;

300,000 m/s = 3.0 x 10⁶ m/s

Thus, the speed of x-rays in scientific notation is 3.0 x 10⁶ m/s.

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explain with the use of diagrams the relationship between resistance,resistivity,cross-sectional area,and length of a wire.

Answers

Answer:

Ohm's LawPower Revisited

An electron traveling through the wires and loads of the external circuit encounters resistance. Resistance is the hindrance to the flow of charge. For an electron, the journey from terminal to terminal is not a direct route. Rather, it is a zigzag path that results from countless collisions with fixed atoms within the conducting material. The electrons encounter resistance - a hindrance to their movement. While the electric potential difference established between the two terminals encourages the movement of charge, it is resistance that discourages it. The rate at which charge flows from terminal to terminal is the result of the combined effect of these two quantities.

Variables Affecting Electrical Resistance

The flow of charge through wires is often compared to the flow of water through pipes. The resistance to the flow of charge in an electric circuit is analogous to the frictional effects between water and the pipe surfaces as well as the resistance offered by obstacles that are present in its path. It is this resistance that hinders the water flow and reduces both its flow rate and its drift speed. Like the resistance to water flow, the total amount of resistance to charge flow within a wire of an electric circuit is affected by some clearly identifiable variables.

First, the total length of the wires will affect the amount of resistance. The longer the wire, the more resistance that there will be. There is a direct relationship between the amount of resistance encountered by charge and the length of wire it must traverse. After all, if resistance occurs as the result of collisions between charge carriers and the atoms of the wire, then there is likely to be more collisions in a longer wire. More collisions mean more resistance.

Second, the cross-sectional area of the wires will affect the amount of resistance. Wider wires have a greater cross-sectional area. Water will flow through a wider pipe at a higher rate than it will flow through a narrow pipe. This can be attributed to the lower amount of resistance that is present in the wider pipe. In the same manner, the wider the wire, the less resistance that there will be to the flow of electric charge. When all other variables are the same, charge will flow at higher rates through wider wires with greater cross-sectional areas than through thinner wires.

A third variable that is known to affect the resistance to charge flow is the material that a wire is made of. Not all materials are created equal in terms of their conductive ability. Some materials are better conductors than others and offer less resistance to the flow of charge. Silver is one of the best conductors but is never used in wires of household circuits due to its cost. Copper and aluminum are among the least expensive materials with suitable conducting ability to permit their use in wires of household circuits. The conducting ability of a material is often indicated by its resistivity. The resistivity of a material is dependent upon the material's electronic structure and its temperature. For most (but not all) materials, resistivity increases with increasing temperature. The table below lists resistivity values for various materials at temperatures of 20 degrees Celsius.

4. Define the terms; I. Frequency II. Wavelength III. Velocity as applied to a periodic wave motion. State the relationship between them. b) Two turning forks have frequencies of 200Hz and 300Hz. Calculate the difference in the wavelengths of the notes they emit. [Speed of sound in air = 330ms-¹]​

Answers

Answer:

Wavelength : It is defined as the distance travelled by a wave during the time a particle of the medium completes one vibration. It is denoted by k. Its SI unit is metre. Frequency: It is the number of occurrences of a repeating event per unit of time. Its SI unit is Hertz (Hz).

Explanation:

What force balances gravity as the balloon sticks to the sticks to the wall?

Answers

Friction Force balances gravity

Answer:

thats answer

Explanation:

please give me a brainlyliest

What force balances gravity as the balloon sticks to the sticks to the wall?

Demario's biology class has a quiz every other Friday. This is the third time Demario has been so worried about other personal matters that he hasn’t done quite as well on the quizzes as he might have otherwise. What has Demario upset is the fact that the professor leaves the room while the students take the quiz, and over half the class is taking the opportunity to cheat. Demario knows personally several of the other students in the class, and some of the ones Demario hangout with are among those who are cheating. Demario knows that a failure to speak to the professor about the cheating will result in his own grade being lower, since the school grades on the curve system. But if Demario does say something to the professor he will be doing his friends and the others a great harm, since cheating is taken very seriously at the school and can lead to expulsion. If Demario doesn’t “turn in” the classmates, the only other alternative is he will get a worse grade than he deserves. He will also be labled as a snitch among is peers and a cheater at the school, either of which Demario has never done. Further, if the professor somehow discovers that Demario is hiding the cheating of others, Demario will be considered an accessory to the cheating, and may be reprimanded for not turning others in, since the school operates on an honor system.

Critical thinking About Ethics Right vs Wrong

What should Demario do?
Should Demario cheat?
Should Demario turn in the cheating classmates?
Should Demario say nothing and not cheat himself?
Be specific in your answer about exactly what Demario should do. (Remember to use one of the three moral theories to solve this dilemma.)

Answers

1. It is unethical for Demario to cheat

2. Demario should not engage in cheating himself

3. Demario should not turn in cheating classmates without careful consideration

4. Reporting classmates may harm relationships, create animosity, and potentially lead to severe disciplinary actions.

What is ethics?

A virtue ethics perspective may also be useful in this circumstance. Demario should make an effort to respect moral principles like honesty, fairness, and integrity while taking the potential repercussions into account and exhibiting empathy for his fellow students.

By employing this strategy, Demario behaves responsibly, deals with the problem subtly, encourages fairness in the educational setting, and upholds his or her own moral standards.

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Convert the following statement to the language used by physicists, "I am cold, please turn on the heat."​

Answers

Answer:

Explanation:fog

Which of the following is a scientific question that can be answered through experimentation?
a. When looking at a map, you ask,c. When sitting with friends in class, you ask, "How
"How are the borders of
many protons does an atom of iron have?"
Germany determined?"
b. When talking to your teacher, d. When looking at a building, you ask, "Will the materials used
you ask, "What is the definition in this building withstand acid rain?"
of matter?"

Answers

b. Is is a scientific question

\(\bold{Hello}\)~

\(\color{purple}\huge\bold\star \underline\mathcal{ \: Answer \: }\star \)

The answer should be B.)

\(\bold\purple{Hopeithelps}\)

\(\bold{Study}\) \(\bold{Well}\) ~

One of the important implications for nuclear energy is for:


A.
agriculture


B.
medicine


C.
industrialization


D.
aeronautics

Answers

Answer:

d

Explanation:The other types of low-level radioactive waste are the tools, protective clothing, wiping cloths, and other disposable items that become contaminated with small amounts of radioactive dust

Answer:

C. Industrialization. Nuclear energy can be used to power industries and factories, providing a reliable, clean and cost-effective form of power. Nuclear energy also has potential applications in desalination, medical isotope production, and even space exploration.

2. A bird flying horizontally at 10 m/s drops a branch. The bird is flying at an altitude of 20 m. Determine
the horizontal displacement it moves relative to where it was dropped.

Answers

Answer:

The horizontal displacement is 20 m.

Explanation:

Given that,

Velocity = 10 m/s

Height = 20 m

We need to calculate the time

Using equation of motion

\(s=ut+\dfrac{1}{2}gt^2\)

Put the value into the formula

\(20=0+\dfrac{1}{2}\times9.8\times t^2\)

\(t^2=\dfrac{20\times2}{9.8}\)

\(t=\sqrt{\dfrac{20\times2}{9.8}}\)

\(t=2.0\ sec\)

We need to calculate the horizontal displacement

Using formula of horizontal displacement

\(\Delta x=v_{x}\times t\)

Put the value into the formula

\(\Delta x=10\times2.0\)

\(\Delta x=20\ m\)

Hence, The horizontal displacement is 20 m.

URGENTTT PLEASE HELPPPP. You put m1 = 1 kg of ice cooled to -20°C into mass m2 = 1 kg of water at 2°C. Both are in a thermally insulated chamber. For water L = 3.33 x 105 J/kg. The specific heat of ice is 2090 J/(kg°C) and of water 4186 J/(kg°C). How much does the ice heat up in order to bring the water down to 0°C?


A. 0.04°C


B. 0.4°C


C. 4°C


D. 10°C


E. 20°C

Answers

Answer:

Explanation:

heat lost by water will be used to increase the temperature of  ice

heat gained by ice

= mass x specific heat  x rise in temperature

1 x 2090 x t

heat lost by water in cooling to 0° C

= mcΔt  where m is mass of water , s is specific heat of water and Δt is fall in temperature .

= 1 x 2 x 4186  

8372

heat lost = heat gained

1 x 2090 x t  = 8372

t = 4°C

There will be a rise of  4 degree in the temperature of ice.  

 

The increase in the temperature of the ice to bring the water to 0 °C is 4 ⁰C.

The given parameters;

mass of the ice, m₁ = 1 kgtemperature of the ice, t₁ = -20°Cmass of the water, m₂ =  1 kgtemperature of the water, t₂ = 2 °C

Apply the principle of conservation of energy to determine the increase in the temperature of the ice to bring the water to 0 °C.

Heat absorbed by the ice = Heat lost by water

\(Q_{ice} = Q_{w}\\\\mc\Delta t_{ice} = mc \Delta t_{w}\\\\1 \times 2090 \times \Delta t = 1 \times 4186 \times (2-0)\\\\2090\Delta t = 8372\\\\\Delta t = \frac{8372}{2090} \\\\\Delta t = 4 \ ^0C\)

Thus, the increase in the temperature of the ice to bring the water to 0 °C is 4 ⁰C.

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Brainlist!! Help!! The nucleus contains protons and neutrons. Being positively charged, the protons repel each other. The nucleus should fly apart due to the repulsive force. Yet, the nuclei of most atoms are stable - explain.

Answers

Answer:

The reason that the nucleus of most atoms does not fall apart despite the oppositely charged protons exerting a repulsive force on each other is the strong nuclear force.

What is the strong nuclear force?

The strong nuclear force is one of the fundamental forces in nature that acts between protons and neutrons in the atomic nucleus. It is a short-range force that is much stronger than the electromagnetic force (which produces the repulsion between protons).

The strong nuclear force is responsible for holding the nucleus together.

Additionally, the ratio of protons to neutrons in a nucleus also affects its stability. Therefore, if there is an imbalance in this ratio, the repulsive force between the protons can become too strong, causing the nucleus to become unstable and undergo radioactive decay.

Overall, the nucleus remains stable due to the balance between the strong nuclear force and the repulsive force between the protons.

What is the value of V^1?

What is the value of V^1?

Answers

\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the Current Electricity.

Since here, A potential divider is setup with two resisters in series, that is 3 ohm and 6 ohm.

As the voltage is always in directly proportional to the resistance,by ohm law,

V = IR, so the increase in Voltage will lead to increase in the resistance too.

hence,

for 6 ohm the voltage is 4 V, then for the 3 ohm it would be ,

V1 = (4/6)*3

==> V1 = 2 Volts,

==> hence the potential V1 = 2V

Mark weighs 375 N and is carrying a full-sized cello as he climbs the stairs to a height of 4 m. It takes him 3 seconds to do this.
How does the amount of work he does change if he were to climb the same flight of stairs again in the same amount of time, but this time without the cello?

A) It depends on the weight of the cello.

B) It remains the same.

C) It increases

D) It decreases.

Answers

Mark's work decreases when he climbs the same flight of stairs again in the same amount of time without the cello.

The correct answer is option D.

The amount of work Mark does depends on the weight of the cello, as well as the distance he climbs and the time it takes. Work is calculated using the formula :

Work = Force × Distance.
In the given scenario, Mark is carrying a full-sized cello while climbing the stairs. The weight of the cello adds to the force he exerts. So, the total force Mark exerts is the weight of the cello plus his own weight (375 N).

When Mark climbs the stairs with the cello, he is doing work against the force of gravity.

The work done is equal to the force exerted multiplied by the distance climbed (375 N + weight of cello) × 4 m.

Now, if Mark were to climb the same flight of stairs again in the same amount of time (3 seconds), but this time without the cello, the amount of work he does would decrease. This is because without the cello, the force exerted would only be Mark's weight (375 N), which is less than the total force exerted with the cello.

Therefore, mark's work decreases.

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During a ball in the cup lab students notice that a ball rolling horizontally on the table pass through two photogates .30 meters apart in 0.133 seconds. They measure the height of the table to be 0.85 meters. Determine the distance away from the tables edge the students must place a cup to catch the ball to complete the activity?

Answers

Answer:

2 meters

Explanation:

When a skater pulls her arms in, it
reduces her moment of inertia from
2.12 kg m² to 0.699 kg-m². If she was
initially spinning 3.25 rad/s, what is
her final angular velocity?

Answers

The skater's final angular velocity is approximately 9.86 rad/s.

The skater's final angular velocity can be calculated using the principle of conservation of angular momentum. The equation for angular momentum is given by:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Initially, the skater has an angular momentum of:

L_initial = I_initial * ω_initial

Substituting the given values:

L_initial = 2.12 kg m² * 3.25 rad/s

The skater's final angular momentum remains the same, as angular momentum is conserved:

L_final = L_initial

The final moment of inertia is given as 0.699 kg m². Therefore, the final angular velocity can be calculated as:

L_final = I_final * ω_final

0.699 kg m² * ω_final = 2.12 kg m² * 3.25 rad/s

Solving for ω_final:

ω_final = (2.12 kg m² * 3.25 rad/s) / 0.699 kg m²

Hence, the skater's final angular velocity is approximately 9.86 rad/s.

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Please help me



Explain why driver age 16-18 are most likely to be involved in traffic accidents

Answers

Answer:Lack of experience.

Explanation:

Research from the CDC points to a few key reasons teen drivers are likely to be involved in car accidents: Lack of experience. Teen drivers have triple the fatal crash risk of older drivers, in part because they do not have the skills to recognize and avoid road hazards.

the ratio of force between two charges in vacuum to that the force between two same charges when a medium is placed between them

Answers

The ratio of the force between two charges in a vacuum to the force between two charges when a medium is placed between them is called relative permittivity

What should you know about relative permittivity?

Relative permittivity has another term dielectric constant. The dielectric constant measures how well a material can store electrical energy in an electric field. Its equation is ε = ε₀ / εᵣ

ε₀ is the vacuum permittivity, and εᵣ is the relative permittivity or dielectric constant of the medium.

The dielectric constant is different depending on the material.

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A radio wave transmits 34.5 W/m2 of power per unit area. A flat surface of area A is perpendicular to the direction of propagation of the wave. Assuming the surface is a perfect absorber, calculate the radiation pressure on it.

Answers

Answer:

1.15*10^-7 N/m²

Explanation:

Radiation pressure is the pressure exerted on any surface, as a result of the exchange of momentum between the object and its electromagnetic field.

The formula to calculate radiation pressure on a perfect absorber is

P = s/c, where

P = radiation pressure

s = intensity of light

c = speed of light

Now, on substituting the values and plugging it into the equation, we have

P = 34.5 / 3*10^8

P = 1.15*10^-7 N/m²

therefore, radiation pressure is found to be 1.15*10^-7 N/m²

Water with a volume flow rate of 0.001 m3/s, flows inside a horizontal pipe with diameter of 1.2 m. If the pipe length is 10m and we assume fully developed internal flow, find the pressure drop across this pipe length.

Answers

Answer:

\(\triangle P=1.95*10^{-4}\)

Explanation:

Mass \(m=0.001\)

Diameter \(d=1.2m\)

Length \(l=10m\)

Generally the equation for Volume flow rate is mathematically given by

 \(Q=AV\)

 \(V=\frac{Q}{\pi/4D^2}\)

 \(V=\frac{0.001}{\pi/4(1.2)^2}\)

 \(V=8.84*10^{-4}\)

Generally the equation for Friction factor is mathematically given by

 \(F=\frac{64}{Re}\)

Where Re

Re=Reynolds Number

 \(Re=\frac{pVD}{\mu}\)

 \(Re=\frac{1000*8.84*10^{-4}*1.2}{1.002*10^{-3}}\)

 \(Re=1040\)

Therefore

 \(F=\frac{64}{Re}\)

 \(F=\frac{64}{1040}\)

 \(F=0.06\)

Generally the equation for Friction factor is mathematically given by

 \(Head loss=\frac{fLv^2}{2dg}\)

 \(H=\frac{0.06*10*(8.9*10^-4)^2}{2*1.2*9.81}\)

 \(H=19.9*10^{-9}\)

Where

\(H=\frac{\triangle P}{\rho g}\)

\(\triangle P=\frac{19.9*10^{-9}}{10^3*(9.81)}\)

\(\triangle P=H*\rho g\)

\(\triangle P=1.95*10^{-4}\)

 

how to find potential energy

Answers

Answer:

The formula for potential energy depends on the force acting on the two objects.

3. A car with a mass of 1600 kg has a kinetic energy of 125 000 J. How fast is it moving?​

Answers

The car is moving at approximately 12.5 meters per second.

The kinetic energy (KE) of an object can be calculated using the formula:

KE = 1/2 * m * \(v^2\)

where

KE = kinetic energy,

m =Mass of the object, and

v = velocity.

In this case, we are given the mass (m) of the car as 1600 kg and the kinetic energy (KE) as 125,000 J. To find the velocity .

Substituting the  values , we have:

125,000 J = 1/2 * 1600 kg *\(v^2\)

Now, we can solve for v by rearranging the equation:

\(v^2\) = (2 * 125,000 J) / 1600 kg

\(v^2\) = 156.25 \(m^2/s^2\)

Taking the square root, we find:

v = √156.25\(m^2/s^2\)

v ≈ 12.5 m/s

Therefore, the car is moving at approximately 12.5 meters per second.

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An aeroplane is circling above an airport in a horizontal circle at a speed of 400 kmh-1.The banking angle of the wings is 20.What is the radius of the circular path?

Answers

Answer: the radius of the circular path is approximately 1637.58 meters.

Explanation:

The centripetal force acting on the airplane is provided by the component of the gravitational force that acts towards the center of the circular path. This component is given by:

F_c = m * g * tan(banking angle)

Where:

F_c is the centripetal force

m is the mass of the airplane

g is the acceleration due to gravity

tan(banking angle) is the tangent of the banking angle

Now, the centripetal force is also given by the formula:

F_c = (m * v^2) / r

Where:

v is the speed of the airplane

r is the radius of the circular path

Equating the two expressions for F_c, we get:

(m * g * tan(banking angle)) = (m * v^2) / r

Canceling out the mass (m) on both sides of the equation, we have:

g * tan(banking angle) = v^2 / r

Solving for r, we get:

r = (v^2) / (g * tan(banking angle))

Substituting the given values:

v = 400 km/h = 400,000 m/h

g = 9.8 m/s^2

banking angle = 20°

Converting the speed to m/s:

v = 400,000 m/h * (1/3600) h/s = 111.11 m/s

Converting the banking angle to radians:

banking angle = 20° * (π/180) rad/° = 0.3491 rad

Now, substituting the values into the formula:

r = (111.11^2) / (9.8 * tan(0.3491))

r ≈ 1637.58 meters

Therefore, the radius of the circular path is approximately 1637.58 meters.

Cart 1 is stationary and has the same mass of cart 2 which collides with cart 1 at a speed of 10 m/s. They do not stick together. Cart 2's velocity after the collision is
a. 5 m/s
b. 20 m/s
c. 0.0 m/s
d. 10 m/s

Answers

C. 0.0 m/s because when cart 2 collided with cart one the energy From the collision would be transferred to cart 1 causing cart 1 to move at 10 m/s

what happened on march 21 every year in the northern hemisphere​

what happened on march 21 every year in the northern hemisphere

Answers

Answer:

B. The Spring equinox

Explanation:

The vernal equinox marks the moment the sun crosses the celestial equator.  The vernal equinox happens on March 19, 20, or 21 every year in the Northern Hemisphere. In the Southern Hemisphere, this same event marks the beginning of fall.  (Source: What Exactly Is The Spring Equinox? - Dictionary.com)

Hopefully this helps.

A woman lives on the eighth floor of an apartment building. She works in a high-rise office building 6.5 blocks away from her apartment on the same street. Her office is on the 14th floor. Assume each story of her apartment building is 4.0 m, each story of her office building is 5.5 m, and a block is 146.6 m long.

Required:
a. Sketch her path.
b. Estimate the distance she travels to work.
c. Find the magnitude of her displacement.

Answers

Answer:

b)   d = 997.9 m ,  c) D = (952.9 i ^ +45 k ^) m ,  D = 953.6 m and θ = 2.7º

Explanation:

In this exercise we must add the distance traveled, remembering that the displacement is a vector and the distance a scalar.

a) The displacement scheme is the woman walks in her building A to descend to the lower floor 4.0 m, we assume that this includes the vertical displacement, until reaching the street level, the displacement is vertical in this part.

Being on the street, she travels the 6.5 blocks to reach the building where she works, they indicate that each block is 146.6 m, this movement is horizontal.

Upon reaching building B, she goes up to his office on the 14th floor where she travels 5.5m on each floor, it is assumed that the distance to go up to the upper floor is included, this displacement is vertical

b and c) Let's find the distance traveled and the displacement

in building A

                          Zₐ = 8 * 4.0

                          Zₐ = -32.0 m k ^

the vector k ^ indicates that the displacement is vertical and the negative sign that it is descending

on the street

                        \(X_{ab}\) = 6.5 146.6

                        X_{ab} = 952.9 m i ^

the vector i ^ indicates that the displacement is the x-axis, we assume that the axis is in the direction of the displacement

in building B

                         \(Z_{b}\) = 14 * 5.5

                         Z_{b} = 77 m k ^

displacement in the vertical axis and in the positive direction

now we calculate the distance traveled,

               d = Zₐ + X_{ab} + Z_{b}

               d = -32 + 952.9 + 77

               d = 997.9 m

note that this value is a scalar

Let's calculate the displacement,

Z axis

           \(Z_{total}\) = Zₐ +  Z_{b}

           Z_{total} = -32 + 77

          Z_{total} = 45 m k ^

X axis

           X_{total} = X_{ab}

           X_{total} = 952.9 m i ^

we can give the result in two ways

a) D = X_total i ^ + Z_total k ^

    D = (952.9 i ^ +45 k ^) m

b) in module form and angles

Let's use the Pythagorean theorem

     D² = \(X_{total}^2\) + \(Z_{total}^2\)

     D = √(952.9² + 45²)

     D = 953.6 m

We use trigonometry

     tan θ = Z / X

     θ = tan⁻¹ (Z / X)

     θ = tan⁻¹ (45 / 952.9)

     θ = 2.7º

this angle is measured from the positive side of the x axis towards the z axis

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