# Relative motion/velocity help

1. Nov 25, 2006

### 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.

2. Nov 25, 2006

$$\vec{v}_{M} = \vec{v}_{B} + \vec{v}_{M,B}$$, 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.

3. Nov 25, 2006

### fsm

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

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

4. Nov 26, 2006

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

5. Nov 26, 2006

### fsm

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

6. Nov 26, 2006

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

7. Nov 26, 2006

### fsm

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

8. Nov 26, 2006

### fsm

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

9. Nov 26, 2006

### fsm

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

10. Nov 26, 2006

### fsm

Could anyone verify this?

11. Nov 27, 2006

### EthanB

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

12. Nov 27, 2006

### fsm

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

13. Nov 27, 2006

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

14. Nov 27, 2006

### fsm

I still get -3.68i

15. Nov 27, 2006

### fsm

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

Last edited: Nov 27, 2006
16. Nov 27, 2006

### fsm

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

17. Nov 27, 2006

### EthanB

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 $$\vec{v}_{M,B}=-3.688\vec{i}+6.761\vec{j}$$.

18. Nov 27, 2006

### fsm

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