a 1.5kg cannon is mounted on top of a 2.0kg cart and loaded with a 52.7 gram ball. The cannon, car, and ball are moving forward with a speed of 1.27m/s. The cannon is ignited and launches a 52.7 gram ball forward with a speed of 75m/s. Determine the post-explosion velocity of the cannon and cart.

Answer 1

m1 =1,5 kg, m2 = 2 kg, m3 =0.0527 kg.
v = 1.27 m/s
u1 =75 m/s,
u2 =?
The law of conservation of linear momentum
(m1+m2+m3) •v = (m1+m2) •u2 + m3•u1,
u2 = {(m1+m2+m3) •v - m3•u1}/(m1+m2) =
={(1.5+2+0.0527)1.27 – 0.0527•75}/(1.5+2)=
=(4.51-3.95)/3.5 = 0.16 m/s (in the previous direction)