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

[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.

 

[radou]

\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.

 

[fsm]

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

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

 

[radou]

\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.

 

[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

 

[radou]

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}.

 

[fsm]

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

 

[fsm]

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

 

[fsm]

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

 

[fsm]

Could anyone verify this?

 

[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

 

[fsm]

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

 

[radou]

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.

 

[fsm]

I still get -3.68i

 

[fsm]

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

 

[fsm]

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

 

[EthanB]

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

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}.

 

[fsm]

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