Final answer:
The person would be traveling at 25 m/s in the opposite direction of the bowling ball's travel, based on the conservation of momentum.
Step-by-step explanation:
The question involves the concept of conservation of momentum, which is a fundamental principle in physics. When the person releases the bowling ball, their combined momentum before release is zero because they are not moving with respect to the ground. After the release, the total momentum should still be zero. The momentum of the bowling ball is its mass times its velocity (200 kg × 10 m/s), which is 2000 kg·m/s in one direction. Therefore, the person must have the same magnitude of momentum in the opposite direction. To find the speed of the person, we divide their momentum by their mass, 2000 kg·m/s ÷ 80 kg, which gives us a speed of 25 m/s in the opposite direction the ball was traveling.