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Kinetic Energy

A 40 kg shell...

Question

A 40 kg shell is moving with a velocity of 72 km/h.It explodes into two pieces, of which one piece of mass 15 kg stops immediately.Calculate the velocity of the other piece.

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Solution

M=40 kg
$\begin{matrix} M_{1} = 15 k g; V_{1} = 0 V_{D} = 72 k m / h = \frac{72 \times 1000}{3600} = 20 m / s M_{2} = M - M_{1} = 40 - 15 = 25 k g \end{matrix}$
$P_{i}$ = initial momentum= $M V_{0}$
$P_{i} = 40 \times 20 = 800 k g m / s$
$P_{f}$ = final momentum
$\begin{matrix} P_{f} = M_{1} V_{1} + M_{2} V_{2} = 15 \times 0 + 25 \times V_{2} P_{f} = 25 V_{2} P_{f} = P_{i} \end{matrix}$ (momentum conservation)
$800 = 25 V_{2}$
$V_{2} = \frac{800}{25} = 32 m / s$

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