Hi student,

Mass of the gun, M = 100kg
Mass of the ball, m = 1kg
Height of the cliff, h = 500m
g = 10ms^−2

Time taken by the ball to reach the ground is
t = √ 2h/g = √2 × 500m/10ms^−2 = 10s
Horizontal distance covered = ut
i.e. 400×u×10
where u is the velocity of the ball.
u = 10ms^−1
According to law of conservation of linear momentum, we get
0 = Mv + μ
v = −mv/M = −(1kg)(40ms−1)/100kg = −0.4ms^−1
-ve sign shows that the direction of recoil of gun is opposite.

Feel free to ask doubts in the Comment Section.

I hope this information helps you.

Good Luck!