A football player kicks a 0.41 kg football initially at rest, and the ball flies through the air. If the kicker's foot was in contact with the ball for 0.051 s and the ball's initial speed after the collision is 21 m/s, what was the magnitude of the average force on the football?

Options

A. 9.7 N
B. 46 N
C. 81 N
D. 210 N

Answer

To find the magnitude of the average force exerted on the football, we can use the relationship between force, change in momentum, and time. Here’s a step-by-step solution:

### Step 1: Understand the problem
The football player kicks a football of mass \( m = 0.41 \, \text{kg} \) which was initially at rest. The ball reaches a speed of \( v_f = 21 \, \text{m/s} \) after being kicked, and the contact time \( t = 0.051 \, \text{s} \).

### Step 2: Calculate the change in momentum
The change in momentum (\( \Delta p \)) can be calculated using the formula:
\[ \Delta p = m \cdot (v_f - v_i) \]
where \( v_i \) is the initial velocity. Since the ball is initially at rest, \( v_i = 0 \, \text{m/s} \).

Substituting the values:
\[ \Delta p = 0.41 \, \text{kg} \cdot (21 \, \text{m/s} - 0 \, \text{m/s}) = 0.41 \, \text{kg} \cdot 21 \, \text{m/s} \]
\[ \Delta p = 8.61 \, \text{kg m/s} \]

### Step 3: Calculate the average force
The average force (\( F_{\text{avg}} \)) can be calculated using the formula:
\[ F_{\text{avg}} = \frac{\Delta p}{t} \]
Substituting the values we have:
\[ F_{\text{avg}} = \frac{8.61 \, \text{kg m/s}}{0.051 \, \text{s}} \]
\[ F_{\text{avg}} \approx 168.8 \, \text{N} \]

### Final Answer
The magnitude of the average force on the football is approximately \( 168.8 \, \text{N} \).

---