Solving the Billiard Balls Problem: Collision Time and Angle Calculation

[rgalvan2]

Two billiard balls are moving on a (coordinatized) pool table according to the respective paths x(t)=(t²-2, \frac{t^2}{2}-1) and y(t)=(t, 5-t²)
where t is time in seconds.

a) When and where do the balls collide?
I found where the 2 graphs intersect to be (2,1) so does that mean at 2 seconds 1 unit of distance away?

b) What is the angle formed by the paths of the balls at the collision point?
This is where I am stuck. Any hints on how to figure this out?

This is due Thursday and any help would be appreciated. Thanks!

 

[Dick]

Yes, they intersect at t=2. Good so far. The last question you asked showed you know how to find tangent vectors to a curve. If you find the two tangent vectors do you know how to find the angle between them (think 'dot product')?