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One particle of mass m is released from rest at a height h above the ground. Simultaneously, a second particle of equal mass m is projected straight up from ground level with initial speed sqrt(2gh). The two collide head-on and stick together (perfectly inelastic). Express the time, measured from the instant of release, at which the merged body reaches the ground, in units of sqrt(h/g).

1. 1/2
2. sqrt(1/2)
3. sqrt(3/4)
4. sqrt(3/2)

Correct answer: sqrt(3/2)

Solution

The particles meet at time t1 = sqrt(h/(2g)) at height 3h/4; after the inelastic collision the combined mass has zero velocity, then falls 3h/4, giving total time sqrt(3h/(2g)) = sqrt(3/2)*sqrt(h/g).

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