High School

A wagon is rolling forward on level ground with negligible friction. A person sitting in the wagon is holding a rock. The total mass of the wagon, rider, and rock is 98.1 kg, and the mass of the rock is 0.267 kg. Initially, the wagon is rolling forward at a speed of 0.465 m/s. The person then throws the rock at a speed of 15.5 m/s, relative to the ground.

Find the speed of the wagon after the rock is thrown:

(a) Directly forward
(b) Directly backward

Answer :

If the rock is thrown directly forward (a) the speed of the wagon after the rock is thrown is approximately 0.428 m/s.

(b) If the rock is thrown directly backward, the speed of the wagon after the rock is thrown is approximately -0.040 m/s.

To find the speed of the wagon after the rock is thrown, we can use the principle of conservation of momentum. According to this principle, the total momentum before the rock is thrown should be equal to the total momentum after the rock is thrown.

(a) When the rock is thrown directly forward:
In this case, the momentum of the rock after it is thrown will be equal to its mass (0.267 kg) multiplied by its final velocity (15.5 m/s). Since there is no external force acting on the wagon, the total momentum of the system after the rock is thrown will remain the same. Therefore, the momentum of the wagon and the rider after the rock is thrown should also be equal to the momentum of the rock.

The momentum of the wagon and the rider can be calculated by multiplying their total mass (98.1 kg) by their final velocity (let's call it v).

So we have:

(0.267 kg) * (15.5 m/s) = (98.1 kg) * v

Solving for v, we find that the speed of the wagon after the rock is thrown directly forward is approximately 0.428 m/s.

(b) When the rock is thrown directly backward:
In this case, the momentum of the rock after it is thrown will be equal to its mass (0.267 kg) multiplied by its final velocity (15.5 m/s) in the opposite direction. Since there is no external force acting on the wagon, the total momentum of the system after the rock is thrown will remain the same. Therefore, the momentum of the wagon and the rider after the rock is thrown should also be equal to the momentum of the rock but in the opposite direction.

Using the same approach as before, we have:
(0.267 kg) * (-15.5 m/s) = (98.1 kg) * v
Solving for v, we find that the speed of the wagon after the rock is thrown directly backward is approximately -0.040 m/s.

Note that the negative sign indicates that the wagon is moving in the opposite direction.

To know more about speed, refer here:

https://brainly.com/question/6280317#

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