A golf ball traveling 3 m/s to the right has a head-oncollision with a stationar

Question

A golf ball traveling 3 m/s to the right has a head-oncollision with a stationary bowling ball in a friction-freeenvironment. If the collision is almost perfectly elastic, thespeed of the golf ball immediately after the collision is: 1. Slightly less than 3m/s. 2. Much less than 3 m/s. 3. Equal to 3 m/s. 4. Slightly greater than 3 m/s. A golf ball traveling 3 m/s to the right has a head-oncollision with a stationary bowling ball in a friction-freeenvironment. If the collision is almost perfectly elastic, thespeed of the golf ball immediately after the collision is: 1. Slightly less than 3m/s. 2. Much less than 3 m/s. 3. Equal to 3 m/s. 4. Slightly greater than 3 m/s.

Explanation / Answer

     initial velocity of the golf ballu1 = 3 m/s      initial velocity of   thebowling ball u2 = 0 m/s       mass of golf ball = m1       mass of bowling ball = m2       here    m 2 >> m1    The system is perfectly elastic   So momentum and energy is conserved       So   , m 1 u1 + m2 u 2 = m 1v 1 + m 2 v 2                  m 1 ( u 1 - v 1 ) = m2( v 2 - u 2 )..............(1)          (1 /2 ) m1 u 12 + (1/2)m2u 22 =( 1 / 2) m 1 v12 +(1/2) m 2 v22                 m 1 ( u 12 - v 12 ) = m2 ( v 22- u22 ) ..............(2)    where v 1 and v2 are finalvelocities of golf ball and bowling ball           divide eq(2) by (1)    u1 + v 1 =    v2 +u 2    finalvelocity of the golf ball is       v 1   = v2 + u 2- u1                                           = v 2 - u 1                                        = v 2 - 3

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