There is a platform weighing 16 tons on the rails. On the platform there is a cannon weighing 3 tons

There is a platform weighing 16 tons on the rails. On the platform there is a cannon weighing 3 tons, directed at an angle of 60 °. Find the speed of a 50kg projectile if, when fired, the platform rolls back 3m in 6s.

Given:
m = 50kg,
M1 = 3t = 3000kg,
M2 = 16t = 16000kg,
α = 60 °,
S = 3m,
t = 6s;
Find: V -?
Let’s apply the law of conservation of momentum along the horizontal axis.
Component of the projectile velocity along this axis:
Vx = V * cos (α);
m * Vx = (M1 + M2) * U,
where U is the speed of the platform with the gun;
U = S / t = 3m / 6s = 0.5m / s;
Vx = U * (M1 + M2) / m = 0.5 * (3000 + 16000) / 50 = 190m / s;
V = Vx / cos (α) = 190 / 0.5 = 380m / s.