A rocket is projected straight up and explodes into three equally massive fragments just as it reaches the top of its flight (refer figure). One of the fragments is observed to come straight down in 2

Question

A rocket is projected straight up and explodes into three equally massive fragments just as it reaches the top of its flight (refer figure). One of the fragments is observed to come straight down in 2 sec, while the other two take 4 sec to come to ground, after the burst. Find the height h (in m) at which the fragmentation occurred.

TestHub · Accepted Answer

At the top the rocket is momentarily at rest; let the downward fragment's vertical speed be $u_{1}$ and each of the other two have vertical speed $u_{2}$ (up). Vertical momentum: $u_{1} = 2 u_{2}$ .

$h = 2 u_{1} + \frac{1}{2} g (2^{2}) = - 4 u_{2} + \frac{1}{2} g (4^{2})$

$h = 4 u_{2} + 20 = - 4 u_{2} + 80 \Rightarrow u_{2} = 7.5, h = 50 m$

Ans. 50

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