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 97.4 kg. The mass of the rock is 0.262 kg. Initially the wagon is rolling forward at a speed of 0.478 m/s. Then the person throws the rock with a speed of 15.3 m/s. Both speeds are relative to the ground. Find the speed of the wagon after the rock is thrown (a) What is the speed of the wagon after the rock is thrown directly forward?

A) 0.319 m/s
B) 0.478 m/s
C) 0.638 m/s
D) 0.797 m/s

Answer 1

The speed of the wagon after the rock is thrown will be the same as its initial speed, which is 0.478 m/s.

Step-by-step explanation:

To find the speed of the wagon after the rock is thrown, we need to apply the conservation of momentum. Initially, the momentum of the system (wagon, rider, and rock) is equal to the mass of the system multiplied by the initial velocity of the wagon. After the rock is thrown, the momentum of the system is equal to the mass of the system multiplied by the final velocity of the wagon.

Using the conservation of momentum:

Initial Momentum = Final Momentum

(Mass of System)(Initial Velocity of Wagon) = (Mass of System)(Final Velocity of Wagon)

(Mass of Wagon + Rider + Rock)(Initial Velocity of Wagon) = (Mass of Wagon + Rider + Rock)(Final Velocity of Wagon)

Since the mass of the rock is very small compared to the mass of the wagon and rider, we can neglect it:

(Mass of Wagon + Rider)(Initial Velocity of Wagon) = (Mass of Wagon + Rider)(Final Velocity of Wagon)

Dividing both sides of the equation by (Mass of Wagon + Rider), we get:

Initial Velocity of Wagon = Final Velocity of Wagon

Therefore, the speed of the wagon after the rock is thrown will be the same as its initial speed, which is 0.478 m/s. Hence, the correct answer is Option B) 0.478 m/s.