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 96.5 kg. The mass of the rock is 0.250 kg. Initially the wagon is rolling forward at a speed of 0.460 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.

______ m/s

Find the speed of the wagon after the rock is thrown directly backward. ____m/s

Apply the rule that the total momentum remains the same.

They should have made it clear if the 16.5 rock velocity is with repect to the ground or the wagon. It probably should be with respect to the wagon.Whichever you assume will make a small difference in the answer.

I hope that is enough information for you to work the problem yourself.

I don't have time to answer everyone's physics questions here and will be helping mainly students who show their own work.

To solve this problem, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, provided there is no external force acting.

Let's start by calculating the initial momentum of the system when the wagon is rolling forward at a speed of 0.460 m/s. The formula for momentum is:

momentum = mass * velocity

The momentum of the wagon, rider, and rock before the rock is thrown can be given by:

momentum initial = (mass of the wagon + mass of the rider + mass of the rock) * initial velocity of the wagon

momentum initial = (96.5 kg) * (0.460 m/s)

Now, let's calculate the momentum of the rock after it is thrown forward. The momentum of the rock can be given by:

momentum final = mass of the rock * final velocity of the rock

momentum final = (0.250 kg) * (16.5 m/s)

The momentum of the wagon after the rock is thrown directly forward will be the same as the momentum of the wagon, rider, and rock before the rock is thrown, since there is no external force acting on the system. Therefore:

momentum final = momentum initial

(0.250 kg) * (16.5 m/s) = (96.5 kg) * final velocity of the wagon

Now we can solve for the final velocity of the wagon:

final velocity of the wagon = (0.250 kg * 16.5 m/s) / 96.5 kg

final velocity of the wagon = 0.0429 m/s (approximately)

So, the speed of the wagon after the rock is thrown directly forward is approximately 0.0429 m/s.

To find the speed of the wagon after the rock is thrown directly backward, we can use the same principle of conservation of momentum. Again, the initial momentum of the system remains the same, but this time the momentum of the rock after it is thrown backward is calculated as:

momentum final = (0.250 kg) * (-16.5 m/s)

Setting momentum final equal to momentum initial, we can solve for the final velocity of the wagon when the rock is thrown backward. This will give us the speed of the wagon after the rock is thrown directly backward.