Hi, I have the follwoing physics question to ask, Plesae help with hints.

"Two people are standing on a 2.5-m-long platform, one at each end. The platform floats parallel to the ground on a cushion of air, like a hovercraft. One person throws a 5.9-kg ball to the other, who catches it. The ball travels nearly horizontally. Excluding the ball, the total mass of the platform and people is 111 kg. Because of the throw, this 111-kg mass recoils. How far does it move before coming to rest again?"

Thx

To solve this question, we can apply the principle of conservation of momentum. The total momentum before the throw is equal to the total momentum after the throw.

Let's consider the two individuals as person A and person B. Person A throws the ball, so the initial momentum of the system (ball, platform, and people) is zero since the ball starts from rest.

After the throw, the ball is caught by person B. Both person A and person B move in the opposite direction in order to conserve momentum.

Here are some hints to solve the problem:

1. Write down the equations for the initial and final momenta:

Initial momentum (before the throw): 0 kg.m/s
Final momentum (after the throw): (mass of the platform + mass of person A + mass of person B) x final velocity

2. Use the equation for momentum, which is the product of mass and velocity:

Momentum = mass x velocity

3. Note that the masses of person A, person B, and the ball are given. The total mass of the platform and people is also given.

4. Calculate the total mass of the platform and people:

Total mass = mass of the platform + mass of person A + mass of person B

5. Determine the final velocity of the platform and people, since the ball is caught and comes to rest. Assume both people move with the same final velocity.

6. Set up the equation for the conservation of momentum, equating the initial and final momenta:

0 = (mass of the platform + mass of person A + mass of person B) x final velocity

7. Solve the equation for the final velocity.

8. Use the equation for displacement: displacement = velocity x time

9. Calculate the time it takes for the system to come to rest using the final velocity and the fact that the distance traveled is equal to the length of the platform.

10. Finally, calculate the displacement by multiplying the time by the final velocity.

I hope these hints help you solve the problem!