# What is the Relative Velocity of Two Cars in Different Directions?

• fsm
In summary, both cars start from the same position and have the same velocity when they are 60 m away from each other. The velocity of the Mustang with respect to the Beetle is 8.12 m/s.
fsm
I need some help with this question:

Two cars, a Volkswagen Beetle travels east @ 5.5 m/s and a Ford Mustang traveling @ 75 degrees north of east @ 7 m/s. Both cars start from the same position and t=0.

a. What is the velocity of the Mustang with respect to the Beetle?
b. What is t when both are 60 m away from each other?
c. What is d after t=5 sec?

I am having a tough time with relative motion. I've read that section a million times. I can solve it by just treating it as a simple vector problem, but the teacher wants using the formula v=v' + V0. So for a do I resolve each vector into its i and j components and add? I'm really confused.

$$\vec{v}_{M} = \vec{v}_{B} + \vec{v}_{M,B}$$, where M stands for Mustang, B for Beetle, and M, B for Mustang relative to Beetle. You know the velocity vectors, since the magnitudes and directions are given. Try to start with that.

$$\vec{v}_{M,B}$$=8.12 m/s @ 124 degrees

Is it now just a kinematics problem for b and c?

fsm said:
$$\vec{v}_{M,B}$$=8.12 m/s @ 124 degrees

Is it now just a kinematics problem for b and c?

How did you get that result? According to my calculations, this is wrong.

7*cos(75)i+7*sin(75)j=5.5i+0j+$$\vec{v}_{M,B}$$

-4.49i+6.76j=$$\vec{v}_{M,B}$$

R=sqrt((-4.49)^2+(6.76)^2)
R=8.12 m/s

theta=arctan(6.76/-4.49)
theta=-56.4 degrees
theta=180-56.4
theta=124 degrees

fsm said:
7*cos(75)i+7*sin(75)j=5.5i+0j+$$\vec{v}_{M,B}$$

Your calculation is wrong - the line above implies
$$\vec{v}_{M,B}=-3.688\vec{i}+6.761\vec{j}$$.

ok I think I found my error. Now I get 7.7 m/s @ 119 degrees.

Well I guess that one is wrong too. I don't see what I'm doing wrong.

$$\vec{v}_{M,B}=7.31\vec{i}+6.761\vec{j}$$ is what I get now.

Could anyone verify this?

You got 7.31 by adding the i hats, rather than subtracting. It should be (sorry, no LaTeX)

(7*cos(75)-5.5)i+(7*sin(75))j=Vrelative

Now when I did that radou said it was wrong. I have no idea now.

fsm said:
Now when I did that radou said it was wrong. I have no idea now.

You didn't do that. You set the equation up correctly, and then miscalculated. EthanB is right, too.

I still get -3.68i

Please could someone tell me what I'm doing wrong? I don't get it.

Last edited:
I'm not trying to be a pest, but anyone?

Your calculation is wrong - the line above implies
$$\vec{v}_{M,B}=-3.688\vec{i}+6.761\vec{j}$$.

fsm said:
I still get -3.68i

That's exactly what you should be getting. I think you misread what radou said: he said that the numbers you got were wrong, that you should've (from your data) gotten $$\vec{v}_{M,B}=-3.688\vec{i}+6.761\vec{j}$$.

I get it now. I just have been working on this problem so much. Thank you both radou and EthanB for your help.

## 1. What is relative motion/velocity?

Relative motion/velocity refers to the movement of an object in relation to another object. It takes into account the position, direction, and speed of both objects to determine their relative motion.

## 2. How is relative motion/velocity calculated?

Relative motion/velocity is calculated by finding the difference in position, direction, and speed between two objects and determining their relative motion based on these factors. It can be calculated using basic algebraic equations and vector calculations.

## 3. What is the difference between relative motion and absolute motion?

The main difference between relative motion and absolute motion is that relative motion takes into account the movement of one object in relation to another, while absolute motion only considers the movement of an object in relation to a fixed point, such as the ground or a stationary object.

## 4. How does relative motion affect everyday life?

Relative motion is an important concept in physics and has many practical applications in everyday life. It helps explain phenomena such as the motion of vehicles, the effects of wind on objects, and the behavior of moving objects in different reference frames.

## 5. Can relative motion/velocity be observed in space?

Yes, relative motion/velocity is observed in space between celestial objects, such as planets, moons, and stars. It is also a crucial concept in understanding orbital mechanics and the movement of spacecraft in relation to other objects in space.

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