Solving the Billiard Balls Problem: Collision Time and Angle Calculation

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SUMMARY

The discussion focuses on solving the Billiard Balls Problem, specifically determining the collision time and angle between two billiard balls on a pool table. The paths of the balls are defined by the equations x(t)=(t^2-2, t^2/2-1) and y(t)=(t, 5-t^2), with a confirmed collision occurring at t=2 seconds at the point (2, 1). To find the angle of collision, participants are advised to calculate the tangent vectors at the collision point and utilize the dot product method to determine the angle between these vectors.

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Two billiard balls are moving on a (coordinatized) pool table according to the respective paths x(t)=(t2-2, [tex]\frac{t^2}{2}[/tex]-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!
 
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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')?
 

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