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Question

A shell of mass 2m fired with a speed u at an angle θ to the horizontal explodes at the highest point of its motion into two fragments of mass m each. If one fragment, falls vertically, the distance at which the other fragment falls from the gun is given by


Correct Answer
A
Your Answer
B
Your Answer
C
Your Answer
D

Solution

The correct option is A
The total momentum of the system must remain conserved after the explosion. Since, at its highest point, the projectile has only a horizontal velocity, we must have
(2m)ucosθ=m×0+m×u
 u=2ucosθ
Thus the horizontal velocity of the other fragment is 2ucosθ. The time taken to reach the highest point (as well as the time taken to fall down from this point) being usinθg, we have
Total horizontal distance covered by the other fragment
=ucosθ×usinθg+2ucosθ×usinθg=32u2sin2θg
Hence the correct choice is (a).

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