Question

A child of mass 31kg is standing on a parade wagon (empty mass M=120kg), which is loaded with 600 gift baskets, each with a mass of 500.g. She throws the baskets off the side one at a time, such that they leave in a horizontal direction, making an angle of 59° with the length of the wagon. There are no frictional losses between the wagon and the road, and the wagon can move only forward and backward. The wagon is originally at rest. By the time the 60th basket is thrown, the speed of the wagon is 2.5m/s. Find the magnitude of the relative velocity of the baskets with respect to the wagon. Assume this velocity is constant.

Answer 1

Given the mass of the child = Mc = 31 kg

mass of teh wagon = Mw = 120 kg

mass of each gift basket = Mb = 500g =0.5kg

As the wagon only can move along the length we have consider the conservation of momentum only in that direction

(Mc+Mw+600Mb)Vx = (Mc+Mw+(600-n)Mb)Vw+ nMb Vbcos

Where Vx is initial velocity of the wagon = 0 , is the angle at which the baskets are thrown out

Vw is velocity of the wagon after the basket is thrown outside in this case after 60th basket is thrown velociy of the wagon is 2.5m/s

   0 = (31+120+540(0.6))2.5 + 60 (0.5)(Vb)cos59

Vb = -1187.5/(30cos59)=-76.85 m/s

relative velocity of the basket with respect to wagon = Vb - Vw = -76.85 -2.5 = -79.35 m/s