First slide

Relative motion based problems

Question

An airplane is flying vertically upwards. When it is at a height of 1000 m above the ground and moving at a speed of 367 m/s., a shot is fired at it with a speed of 567 m/s from a point directly below it. What should be the acceleration of airplane so that it may escape from being hit?

Moderate

A

>5 $m / s^{2}$
B

>10 $m / s^{2}$
C

<10 $m / s^{2}$
D

Not possible

Solution

${V^{2}}_{rel} - {u^{2}}_{rel} = 2 a_{rel} S$
$0 = {(200)}^{2} - 2 (a_{r e l}) (1000)$
or $a_{r e l} = 20 m / s^{2}$

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