Question

A wagon is rolling forward on level ground. Friction is negligible. The person sitting in the wagon is holding a rock. The total mass of the wagon, rider, and rock is 99.0 kg. The mass of the rock is 0.261 kg. Initially the wagon is rolling forward at a speed of 0.519 m/s. Then the person throws the rock with a speed of 15.9 m/s. Both speeds are relative to the ground. Find the speed of the wagon after the rock is thrown (a) directly forward in one case and (b) directly backward in another.

Answer 1

Explanation:

It is given that,

The total mass of the wagon, rider and the rock is 99 kg

The mass of the rock is 0.261 kg.

The initial speed of the wagon, u = 0.519 m/s

Speed of the rock, u' = 15.9 m/s

(a) Let v is the speed of the wagon after the rock is thrown directly in forward direction.

The momentum will remain constant. Using the conservation of momentum as :

$99\times 0.261=0.261\times 15.9+(99-0.261)v$

v = 0.22 m/s

(b) Let v' is the speed of the wagon after the rock is thrown directly in opposite direction, u' = -15.9 m/s

$99\times 0.261=0.261\times (-15.9)+(99-0.261)v$

v' = 0.304 m/s

Hence, this is the required solution.