A billiard ball rolling across a table at 1.35 m/s makes a head-on elastic colli

Question

A billiard ball rolling across a table at 1.35 m/s makes a head-on elastic collision with an identical ball. Find the speed of each ball after the collision when each of the following occurs.

(a) The second ball is initially at rest.

(b) The second ball is moving toward the first at a speed of 1.15 m/s.

first ball ____ m/s

second ball_____ m/s

(c) The second ball is moving away from the first at a speed of 1.10 m/s.

first ball______ m/s

second ball _____ m/s

Explanation / Answer

final velocities during the eleastic collision v1 = (m1-m2)u1/(m1+m2)+2m2u2/(m1+m2)

v2 = 2m1u1/(m1+m2)+(m2-m1)u2/(m1+m2)

a) u2 = 0 and m1 = m2

v1 = 0

v2 = 2m*1.35/2m = 1.35 m/s

b) v1 = -2m*1.15/2m = -1.15 m/s

v2 = 2m*1.35/2m = 1.35 m/s

c) v1 = 2m*1.1/2m = 1.1 m/s

v2 = 2m*1.35/2m = 1.35 m/s

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