Answer :
Final answer:
The question relates to the conservation of momentum in a system, where a 6.0-kg ball is thrown from a platform, causing the platform and people with a total mass of 118 kg to recoil. Without further forces, the platform would continue moving indefinitely. The recoil distance cannot be computed without the initial velocity of the thrown ball.
Explanation:
The question involves the concept of conservation of momentum, which is a fundamental principle in physics. When the 6.0-kg ball is thrown, the 118-kg mass of the platform and people must recoil in the opposite direction to conserve momentum because the system is initially at rest. The momentum of the thrown ball is equal and opposite to the momentum of the recoiling platform and people. Assuming that no external forces act on the system (such as friction due to the air cushion), the platform and the people will not come to rest again unless acted upon by another force. Therefore, without additional forces, they would continue moving indefinitely. To find the recoil speed, we can use the formula:
momentum of ball = momentum of platform and people.
Given that momentum is mass times velocity (p = mv), the velocity of the recoiling system (vrecoil) can be found by:
(mass of ball) × (velocity of ball) = (mass of platform and people) × (velocity of recoil)
Thus:
6.0 kg × 0 m/s = 118 kg × vrecoil
Since the ball is initially thrown at a non-zero velocity, we would need that velocity to calculate the recoil velocity. However, because the velocity of the thrown ball is not given in this instance, we cannot determine how far the platform moves before coming to rest again.
