A 15-kg object sitting at rest is struck elastically in a head-on collision with a 12-kg object initially moving at +3.0 m/s.Find the final velocity of the 15-kg object after the collision.

Question

Quizplus · Accepted Answer

Using conservation of momentum: 
(m1)(v1i) + (m2)(v2i) = (m1)(v1f) + (m2)(v2f)
(15 kg)(0 m/s) + (12 kg)(3.0 m/s) = (15 kg)(v1f) + (12 kg)(v2f)
Solving for v1f:
v1f = (m2)(v2i - v2f) / m1
v1f = (12 kg)(3.0 m/s - v2f) / 15 kg
v1f = 2.4 m/s - 0.8v2f
Using conservation of kinetic energy: 
(1/2)(m1)(v1i)^2 + (1/2)(m2)(v2i)^2 = (1/2)(m1)(v1f)^2 + (1/2)(m2)(v2f)^2
Substituting the values, we can solve for v2f:
v2f = 6/4 = 1.5 m/s 
Now, substituting v2f into the equation for v1f:
v1f = 2.4 m/s - 0.8(1.5 m/s) = +3.0 m/s
Therefore, the final velocity of the 15-kg object is +3.0 m/s.

A 15-Kg Object Sitting at Rest Is Struck Elastically in a Head-On