The 12Mg truck drives onto the 350Mg barge the dock at 20 km

The 12-Mg truck drives onto the 350-Mg barge the dock at 20 km/h and brakes to a stop on the deck. The barge is free to move in the water, which offers negligible resistance to motion at low speeds. Calculate the speed of the bar after the truck has come to rest on it.

Solution

mass of the truck, m1 = 12000 kg

mass of the barge, m2 = 350000 kg

initial velocity of truck, u1 = 20 kmph = 20x5/18 = 5.55 m/s

initial velocity of barge, u2 = 0 kmph = 0 m/s

final velocity of truck, v1 = 0 kmph = 0 m/s

final velocity of barge, v2 = x (say)

According to law of conservation of momentum,

initial momentum = final momentum

m1u1 + m2u2 = m1v1 + m2v2

12000x5.55 + 350000x0 = 12000x0 + 350000xV₂

(12000x5.55)/350000 = v₂

v₂ = 0.19047 m/s x 18/5 = 0.6857 kmph