Question

One object moves in the positive x direction with speed v. Another object moves in the opposite direction with the same speed but with one half the mass of the first object. The two objects have a completely inelastic collision. What is the final x component of the velocity?

Answer 1

Mass of first object = m

Mass of second object = m/2

Velocity of the first object before the collision = V

Velocity of the second object before the collision = -V (Negative as is directed in the negative x-direction)

The collision is completely inelastic, therefore both the objects stick to each other after the collision.

Velocity of both the objects after the collision = V_f

By conservation of linear momentum,

mV + (m/2)(-V) = (m + m/2)V_f

mV - mV/2 = 3mV_f/2

V_f = V/3

Final X-component of the velocity of the two objects = V/3