Question

A 200-ton artillery gun is mounted on a 100-ton railroad car that moves on an east-west track with negligible friction. A metric ton is 1000 kg. If the soldiers did not set the brakes nor mount the car to the ground before shooting the gun, and it fired a 100-kg shell eastward with a velocity of 1600 m/s at an angle of 20^o above the horizontal, what would the railroad car with the gun be doing after firing the shell?

Answer 1

let M = 200 + 100

= 300 ton

= 300*1000 kg (total mass of gun and car)

mass of shell, m = 100 kg

v_shell = 1600 m/s

let v is the velocity of the railroad car with the gun after firing the shell.

Apply conservation of momentum in horizontal direction.

total momentum after firing = total momentum before firing

M*v + m*v_shell*cos(20) = 0

M*v = -m*v_shell*cos(20)

v = -m*v_shell*cos(20)/M

= -100*1600*cos(20)/(300*1000)

= -0.501 m/s

here negative sign indicates West direction.

so, the railroad car with the gun moves with speed 0.501 m/s in west direction after firing the shell.