A 50-g ball moving at 10 m/s in the +x direction suddenly collides head-on with a stationary ball of mass 100 g. If the collision is perfectly elastic, what is the velocity of each ball immediately after the collision?
A) +3.3 m/s,-6.7 m/s
B) -3.3m/s,+6.7 m/s
C) -6.7 m/s,+3.3 m/s
D) +6.7 m/s,-3.3 m/s

Question

A  50-g ball moving at  10 m/s in the  +x  direction suddenly collides head-on with a stationary ball of mass  100 g. If the collision is perfectly elastic, what is the velocity of each ball immediately after the collision?
A)  +3.3 m/s,-6.7 m/s
B)  -3.3m/s,+6.7 m/s
C)  -6.7 m/s,+3.3 m/s
D)  +6.7 m/s,-3.3 m/s

Quizplus · Accepted Answer

In a perfectly elastic collision, both momentum and kinetic energy are conserved. For the 50-g ball (m1) moving at 10 m/s (v1) colliding with a stationary 100-g ball (m2), the final velocities (v1' and v2') can be found using the conservation laws. The equations for conservation of momentum and kinetic energy are: m1v1 + m2v2 = m1v1' + m2v2' and 0.5m1v1^2 + 0.5m2v2^2 = 0.5m1v1'^2 + 0.5m2v2'^2. Solving these equations with v2 = 0 (since the second ball is initially stationary) gives v1' = -3.3 m/s and v2' = +6.7 m/s, indicating that the first ball reverses direction and the second ball moves forward.

A 50-G Ball Moving at 10 M/s in the