Two people are standing on a 2.2-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 6.0-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 119 kg. Because of the throw, this 119-kg mass recoils. How far does it move before coming to rest again?
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the throw should be equal to the total momentum after the throw.
The momentum of an object is defined as the product of its mass and velocity. In this case, we need to consider the momentum of the ball and the momentum of the platform and people.
Let's assume that the initial velocity of the ball is v. Since the ball is caught by the other person at the same height, the final velocity of the ball is also v. The mass of the ball is 6.0 kg.
The initial momentum of the ball is given by: momentum_initial = mass * velocity_initial = 6.0 kg * v
The total mass of the platform and people is 119 kg. Since the platform and people are initially at rest, their initial momentum is zero.
The final momentum of the platform and people is given by: momentum_final = mass * velocity_final = 119 kg * velocity_final
According to the principle of conservation of momentum, the total momentum before the throw should be equal to the total momentum after the throw:
momentum_initial = momentum_final
6.0 kg * v = 119 kg * velocity_final
To find the velocity_final, we need to know the mass of the ball and the velocity_initial. However, this information is not provided in the given question. Without this information, we cannot determine the distance the platform and people move before coming to rest again.
To solve the problem completely, we need additional information.