Q31 of 42 Page 34

A 100 kg gun fires a ball of 1kg horizontally from a cliff of height 500m. It falls on the ground at a distance of 400m from the bottom of the cliff. Find the recoil velocity of the gun. (acceleration due to gravity = 10 m s-2)

Given, the height of the cliff is,

Height of the cliff, h=500 m


Mass of the ball, m= 1 kg


Mass of the gun, M=100 kg


Range of the ball, R= 400 m


Acceleration due to gravity, g= 10 m s-2


Let the final velocity of the ball be u and the of the gun be v.


Now we know, time of flight is




And range is given by:



So, u=400/10 = 40 m s-2


Therefore, the velocity is:





The recoil velocity of the gun is 0.4 m s-1.


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