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Q.

A shell is fired from a cannon with a velocity V at an angle $θ$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. The speed of the other piece immediately after the explosion is

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a

$3 V \cos θ$

b

$2 V \cos θ$

c

$\frac{3}{2} V \cos θ$

d

$V \cos θ$

answer is A.

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Detailed Solution

By the principal of conservation of momentum,

$mVcosθ = \frac{m}{2} (- Vcosθ) + \frac{m}{2} V^{'}$

$\Rightarrow V^{'} = 3 Vcosθ$

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A shell is fired from a cannon with a velocity V at an angle θ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. The speed of the other piece immediately after the explosion is