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 93.5 kg. The mass of the rock is 0.310 kg. Initially the wagon is rolling forward at a speed of 0.540 m/s. Then the person throws the rock with a speed of 16.5 m/s. Both speeds are relative to the ground. Find the speed of the wagon after the rock is thrown directly forward.

Given Data

Total mass=93.5 kg

Rock mass=0.310 kg

Initially wagon speed=0.540 m/s

rock speed=16.5 m/s

To Find

The speed of the wagon

Solution

As the wagon rolls, momentum is given as

P=mv

where

m is mass

v is speed

put the values

P=93.5kg * 0.540 m/s

P = 50.49 kg*m/s

Now we have to find the momentum of rock

momentum of rock = mv

momentum of rock = (0.310kg) * (16.5 m/s)

momentum of rock = 5.115 kg*m/s

From the conservation of momentum we can find the wagons momentum So

wagon momentum=50.49 - 5.115 = 45.375 kg*m/s

Speed of wagon = wagon momentum / (total mass-rock mass)

Speed of wagon=45.375 / (93.5-0.310)

Speed of wagon = 0.487 m/s

Throwing rock backward,

momentum of wagon = 50.49+5.115 = 55.605 kg*m/s

Speed of wagon = wagon momentum / (total mass-rock mass)

speed of wagon = 55.605 kg*m/s / (93.5kg-0.310kg)

speed of wagon = 0.5967 m/s