Final answer:
The impulse given to the ball by the floor is calculated by finding the change in momentum due to collision, which involves calculating the velocity before impact and after rebound using the conservation of energy. The calculated impulse is 1.3935 kgm/s, which doesn't match the provided options.
Step-by-step explanation:
To determine the impulse given to the ball by the floor, we must first find the change in the ball's momentum due to the collision. Impulse is equal to the change in momentum and can be calculated using the velocities before and after the collision. Given the data:
- Mass of the ball, m = 0.150 kg
- Initial height, h1 = 1.25 m
- Rebound height, h2 = 0.960 m
We can use the conservation of energy to find the speed of the ball just before it hits the floor and just after it rebounds.
Velocity before impact:
Using v2 = 2gh, where g = 9.81 m/s2 (acceleration due to gravity), the velocity just before impact v1 = sqrt(2 * g * h1) = sqrt(2 * 9.81 m/s2 * 1.25 m) = 4.95 m/s (downwards).
Velocity after rebound:
Similarly, the velocity just after rebound v2 = sqrt(2 * g * h2) = sqrt(2 * 9.81 m/s2 * 0.960 m) = 4.34 m/s (upwards).
Since the ball changes direction, we need to consider the velocities as vectors. Thus, the change in velocity Δv = v2 + v1 = 4.34 m/s + 4.95 m/s = 9.29 m/s.
The impulse I imparted on the ball is then I = mΔv = 0.150 kg * 9.29 m/s = 1.3935 kgm/s. However, since none of the answer choices match this value, it is likely that the question contains a miscalculation or there has been a mistake somewhere in the computation. The closest choice to the correct calculation would be (a) 1.01 kgm/s, but we should double-check the figures and calculations before selecting our answer.