Final answer:
The momentum of the ball at maximum height is 0 kg·m/s since its velocity is 0 m/s at that point. Halfway to maximum height, the momentum is positive but less than the initial momentum of 1.5 kg·m/s.
Step-by-step explanation:
The question involves finding the momentum of a ball at different points during its upward trajectory. When the ball reaches its maximum height, its vertical velocity is 0 m/s. Since momentum (p) is the product of mass (m) and velocity (v), at the maximum height, the momentum is 0.10 kg × 0 m/s = 0 kg·m/s. Thus, option (a) 1.5 kg·m/s is incorrect because the correct value should be 0 kg·m/s.
Halfway to maximum height, the ball still has upward velocity, but it is less than the initial velocity due to the deceleration from gravity. Without additional information about the exact velocity at this point, we cannot solve for an exact momentum value. However, we can conclude that the momentum will be positive and less than the initial momentum. The initial momentum can be calculated as mass times the initial velocity: 0.10 kg × 15 m/s = 1.5 kg·m/s. So, halfway up, the momentum will be less than 1.5 kg·m/s but greater than 0 kg·m/s.