Solving the Billiard Balls Problem: Collision Time and Angle Calculation

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In summary, the two billiard balls collide at the point (2,1) on the pool table after 2 seconds. To find the angle formed by the paths of the balls at the collision point, you can use the tangent vectors and calculate the dot product between them.
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rgalvan2
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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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  • #2
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')?
 

FAQ: Solving the Billiard Balls Problem: Collision Time and Angle Calculation

What is the "Billiard Balls problem"?

The Billiard Balls problem is a mathematical puzzle that involves arranging a certain number of identical billiard balls in a triangular rack formation. The goal is to determine the total number of balls in the rack based on the number of rows in the formation.

Who first proposed this problem?

The Billiard Balls problem is attributed to mathematician, physicist, and astronomer Sir Isaac Newton, who posed it in the 17th century.

What is the solution to the Billiard Balls problem?

The solution to the Billiard Balls problem is given by the formula (n+1)(n+2)/2, where n is the number of rows in the triangular formation. This formula yields the total number of balls in the rack, including those in the last row that may be partially filled.

What is the significance of the Billiard Balls problem?

The Billiard Balls problem is not only a fun mathematical puzzle, but it also has important applications in fields such as crystallography and number theory. It also helps to develop logical and critical thinking skills.

Are there variations of the Billiard Balls problem?

Yes, there are many variations of the Billiard Balls problem, such as changing the shape of the rack or using different types of objects instead of billiard balls. Some variations may have different solutions or may require different approaches to solve.

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