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PhysicsQ&A LibraryA cue ball of mass m1 = 0.325 kg is shot at another billiard ball, with mass m2 = 0.505 kg, which is at rest. The cue ball has an initial speed of v = 7.5 m/s in the positive direction. Assume that the collision is elastic and exactly head-on.(a) Write an expression for the horizontal component of the billiard ball's velocity, v2f, after the collision, in terms of the other variables of the problem.(b) What is this velocity, in meters per second?(c) Write an expression for the horizontal component of the cue ball's velocity, v1f, after the collision.(d) What is the horizontal component of the cue ball's final velocity, in meters per second?Question

Asked Nov 7, 2019

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A cue ball of mass *m*_{1} = 0.325 kg is shot at another billiard ball, with mass *m*_{2} = 0.505 kg, which is at rest. The cue ball has an initial speed of *v* = 7.5 m/s in the positive direction. Assume that the collision is elastic and exactly head-on.

**(a) ** Write an expression for the horizontal component of the billiard ball's velocity, *v*_{2f}, after the collision, in terms of the other variables of the problem.

**(b) ** What is this velocity, in meters per second?

**(c)** Write an expression for the horizontal component of the cue ball's velocity, *v*_{1f}, after the collision.

**(d) ** What is the horizontal component of the cue ball's final velocity, in meters per second?

Step 1

(a)Since the collision is elastic, total linear momentum as well as the total kinetic energy of the system must be conserved.

Step 2

Rearranging equation (3)

Step 3

(b) Substitute the numerical v...

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