Final answer:
To find the average force exerted on a ball during a kick, one can use the impulse-momentum theorem. The change in momentum of the ball is calculated and divided by the time interval to get the force. However, none of the answer choices provided match the calculated value exactly, indicating a potential error.
Step-by-step explanation:
The question involves calculating the average force exerted on a ball during a kicking event. To find this, we use the impulse-momentum theorem, which states that the change in momentum of an object is equal to the impulse applied to it. The impulse can be calculated as the product of the average force and the time interval during which the force acts.
The change in momentum (Δp) is the final momentum minus the initial momentum, given by:
Δp = m(v_f - v_i)
Where:
- m is the mass of the ball
- v_f is the final velocity of the ball
- v_i is the initial velocity of the ball
Substituting the values given in the question:
Δp = 0.25 kg (-12 m/s - (+6.2 m/s))
Δp = 0.25 kg (-18.2 m/s)
Δp = -4.55 kg·m/s
The impulse (J) is also equal to:
J = Force (F) × time (t)
Therefore:
Force = Δp / t
Force = -4.55 kg·m/s / 0.021 s
Force = -216.67 N (The negative sign indicates the force direction is opposite to the initial velocity)
However, the question asks for the magnitude of the average force, so we take the absolute value:
|Force| = 216.67 N
The closest answer option to our calculated value is (b) 100 N, which is incorrect. The exact calculated value is not listed in the options provided, so it appears there is an error either in the calculation or in the answer choices.