A traditional Bugghi (a luxury cart drawn by horses) features a wooden plate attached to its rear where a person can sit. A bugghi with a mass of 200 kg is travelling at 10 km/h . As it overtakes a school boy walking at 4 km/h , the boy sits on the wooden plate. Given that the boy's mass is 25 kg , determine the new velocity of the bugghi.

Step-by-step solution

Let the mass of the bugghi be M = 200 kg and its initial velocity be v₁ = 10 km/h . Let the mass of the boy be m = 25 kg and his initial velocity be v₂ = 4 km/h . Since no external force acts on the system in the horizontal direction during the process of the boy sitting on the bugghi, the linear momentum of the system is conserved. Applying the principle of conservation of linear momentum: M v₁ + m v₂ = (M + m) v_ new 200 10 + 25 4 = (200 + 25) v_ new 2000 + 100 = 225 v_ new 2100 = 225 v_ new v_ new = 2100 225 v_