Final answer:
The impulse delivered to the football is -7.5 kgm/s, and the average force exerted on the receiver is 375 N. Impulse is computed by the change in momentum, and average force is the impulse divided by the time interval during which it acts.
Step-by-step explanation:
The student asks to calculate the impulse delivered to a football and the average force exerted on a receiver. The impulse can be found by using the formula impulse (J) = mass (m) × change in velocity (Δv), while the average force (F) can be calculated by dividing the impulse by the time interval (Δt) over which the force acts.
In this case:
- Mass of the football, m = 0.5 kg
- Initial velocity, vi = 15 m/s (east)
- Final velocity, vf = 0 m/s
- Time interval, Δt = 0.02 s
Impulse to the ball (J) = m × (Δv) = 0.5 kg × (0 - 15 m/s) = -7.5 kg·m/s. The negative sign indicates direction opposite to the initial velocity.
Average force (F) = Impulse (ΔJ) / Time interval (Δt) = -7.5 kg·m/s / 0.02 s = -375 N. The negative sign indicates direction opposite to the initial velocity, which is not necessary when considering magnitude only.
Therefore, the correct answer is: a) -7.5 kg·m/s, b) 375 N