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

A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height

1.	A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500 m. It falls on the ground at a distance of 400 m from bottom of the cliff. Find the recoil velocity of the gun. (acceleration due to gravity = 10 ms^(-2) )
Answer» Solution :Massof gun`m_(1) =100kg` mass of BALL`m_(2)=1 kg` Height of thecliffh =500 m x = 400m Initiallyverticalcomponentof velocityis zero(in downarddirection ) `h= (1)/(2)gt^(2)` `500 = 5t^(2)` `t= SQRT(100) = 10 s` Forhorizontalmotionof ball x= ut `u = (x )/( t ) = (400)/(10) =40 m//s` Letv isrecoil VELOCITY of gun BYLAW of conservation of linearmomentum `m_(1)v= m_(2) u` `v= (m_(2) u )/( m_(1)) = (1)/(100)xx 40 = 0.4 m//s`