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Linear Momentum

A projectile ...

Question

A projectile of mass $50 k g$ is shot vertically upwards with a velocity of $100 m / s$ . After 5 seconds the projectile explodes into two fragments, one of which (mass $20 k g$ ) travels vertically up with a velocity of $150 m / s$ . What will be the velocity of the other fragment at this moment? $(g = 9.8 {m / s}^{2})$

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Solution

Initial velocity = 100 $m / s$

Velocity after 5 second :

V = u + at

V = 100 - 9.8 ( 5 )

V = 51 $m / s$

According to the law of conservation of linear momentum,

initial momentum = final momentum

MV = $M_{1} V_{1} + M_{2} V_{2}$

M = 50 kg

$M_{1}$ = 20 kg

$M_{2}$ = 30 kg

$V_{1} =$ 150 $m / s$

on substituting the value ,

We get.

$V_{2} = - 15 m / s$

negative sing signifies that other fragment is moving downward

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