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From the top of a tower of height H, a body of mass m is dropped and simultaneously a body of mass M is projected vertically upward with speed u. If M reaches its highest point before m hits the ground, find the maximum height of the centre of mass of the system measured from the ground.

1. H + u²/(2g)
2. u²/(2g)
3. H + (1/(2g)) (Mu/(m + M))²
4. H + (1/(2g)) (mu/(m + M))²

Correct answer: H + (1/(2g)) (Mu/(m + M))²

Solution

Only gravity acts on both bodies, so the CM moves with initial upward speed Mu/(m+M) and acceleration g down; its maximum rise above the tower top is (Mu/(m+M))²/(2g), giving max height H + (1/(2g))(Mu/(m+M))².

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