Final Answer:
The average force exerted on the stationary football by the footballer's foot, calculated using the impulse-momentum theorem, is 200 N. This is derived by dividing the change in momentum by the contact time, providing a measure of the force applied during the brief interaction.
Explanation:
The average force exerted on the ball by the footballer's foot can be calculated using the impulse-momentum theorem, which states that the impulse imparted to an object is equal to the change in its momentum. Mathematically, impulse (J) is given by the product of force (F) and the time (Δt) over which it acts: J = F * Δt. The change in momentum (Δp) of the ball is equal to its mass (m) multiplied by the change in velocity (Δv): Δp = m * Δv.
The average force (F) can be expressed as the ratio of impulse to time: F = Δp / Δt. Given that the mass of the ball is 0.40 kg, the initial velocity is 25 m/s, and the time of contact is 0.050 s, we can calculate the change in momentum (Δp) using the formula: Δp = m * Δv = m * (final velocity - initial velocity). After obtaining Δp, the average force (F) can be determined by dividing Δp by the contact time Δt.
In this case, the calculations yield an average force of 200 N, leading to the final answer of 200 N (Option C). The force is a measure of how much the ball's momentum changes during the brief contact with the footballer's foot. A higher force results in a more significant change in momentum, contributing to the ball's acceleration.
