Calculating Relative Motion and Vectors for Moving Cars

[southernbelle]

Homework Statement

Car A's velocity varies as Va=3t^2i + 3tj
Car B's velocity varies as Vb= -4ti + 4t^2j
Both car's start at t=0.

a) Find the position of Car A with respect to Car B at t=1 second.
b) Find the velocity of Car B with respecto Car A at t=2.

The Attempt at a Solution

a) I began by finding the antiderivative of Va and Vb.
I got v'(A)=t^3i + 3/2t^2i and
v'(B) = -2t^2i + 4/3t^3

Then I plugged in 1 for t and subtracted Car A - Car B.
I got 3i - 1/6j
Did I do that right?

b) I basically did the same thing except I used to orginial equations, plugged in 2 for t, abd subtracted Car B- Car A.
I came up with 4i - 24j

Did I do those problems correctly?

 

[Perillux]

well you messed up with the components i and j in your integrals. You have 2 i's and no j for the first one, and no j in the second one.
But, I think you just typed it wrong so don't worry about it.

For part a I got the same thing you did except positive. I got 3i + 1/6j
and I didn't do the second part, but you might want to double check that that one isn't also positive, like 4i + 24j

 

[southernbelle]

Okay, so instead of subtracting vectors in relative motion, I should add them?

When I plotted the vectors I did positive js.

Oh and sorry about the mistype!

 

[Perillux]

no, you still subtract them. But should get I think it was 9/6j - 8/6j = 1/6j positive.
So you did it right, maybe you just switched the vectors or got confused somewhere.

 

[southernbelle]

Ok, so, when I work out the components of the vectors, that is what I should subtract?

For instance, I would do:
3/2j - 4/3j

Because I have been adding both i's and both j's and then subtracting those numbers from each other.

 

[Perillux]

either way works.
because if you have say 4i + 6j
and I want to subtract the vector 2i + 3j
it would be written like
(4i + 6j) - (2i + 3j)
which is equal to
4i + 6j - 2i - 3j = 2i + 3j

But to make it easier on yourself you can use a different form of representing vectors: (i, j) without the plus.

 

[southernbelle]

Okay, thank you!
I don't know how to mark this as solved.