Question

# A wagon is rolling forward on level ground. Friction is negligible. The person sitting in the...

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 kg. The mass of the rock is 0.30 kg. Initially the wagon is rolling forward at a speed of 0.46 m/s. Then the person throws the rock with a speed of 15 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.

here,

mass of rock , m1 = 0.3 kg

mass of wagon and rider , m2 = 90 - m1 = 89.7 kg

initial speed of wagon , rider and rock , u = 0.46 m/s

a)

when final speed of rock , v1 = 15 m/s

let the final speed of wagon be v2

using conservation of momentum

(m1 + m2) * u = m1 * v1 + m2 * v2

(90) * 0.47 = 0.3 * 15 + 89.7 * v2

solving for v2

v2 = 0.42 m/s

b)

when final speed of rock , v1 = - 15 m/s

let the final speed of wagon be v2

using conservation of momentum

(m1 + m2) * u = m1 * v1 + m2 * v2

(90) * 0.47 = - 0.3 * 15 + 89.7 * v2

solving for v2

v2 = 0.52 m/s