Final answer:
The resulting velocity of the 78 kg ice skater after throwing the 6.0 kg bowling ball with a velocity of -3.0 m/s is 0.23 m/s in the direction opposite to the thrown ball, based on the conservation of momentum.
Step-by-step explanation:
The question is asking to find the resulting velocity of a 78 kg ice skater after throwing a 6.0 kg bowling ball with a horizontal velocity of -3.0 m/s. To solve this problem, we will apply the principle of conservation of momentum. The initial momentum of the system (skater and ball) is zero because the skater is at rest. After throwing the ball, the total momentum of the system must still be zero, because there are no external forces in the horizontal direction.
The momentum of the ball after being thrown is its mass times its velocity, which is 6.0 kg × (-3.0 m/s) = -18.0 kg·m/s. The negative sign indicates that the ball is moving in the negative direction. For the total momentum to remain zero, the skater must have an equal and opposite momentum, so we have: skater's mass × skater's velocity = 18.0 kg·m/s. Therefore, skater's velocity = 18.0 kg·m/s / 78 kg = 0.23 m/s in the positive direction (opposite to the direction of the ball).