During a football match, the ball shot towards the goal struck the defender foot at the speed of `10 ms^-1` and it bounces back at `20 ms^-1` IF the time of impact was 0.2s and mass of the ball is `1//2kg` then average force exerted by defender on the ball is

Options

A. 75N
B. 35N
C. 50N
D. 40N

Explanation

To find the average force exerted by the defender on the football, we can follow these steps:

### Step 1: Identify the given values
- Initial speed of the ball (u) = 10 m/s (towards the defender)
- Final speed of the ball (v) = -20 m/s (bouncing back, hence negative)
- Mass of the ball (m) = 0.5 kg
- Time of impact (Δt) = 0.2 s

### Step 2: Calculate the change in momentum (ΔP)
The change in momentum (ΔP) is given by the formula:
\[ \Delta P = m \cdot v - m \cdot u \]
Substituting the values:
\[ \Delta P = 0.5 \cdot (-20) - 0.5 \cdot (10) \]
Calculating this:
\[ \Delta P = -10 - 5 = -15 \, \text{kg m/s} \]

### Step 3: Calculate the average force (F)
The average force can be calculated using the formula:
\[ F = \frac{\Delta P}{\Delta t} \]
Substituting the values:
\[ F = \frac{-15}{0.2} \]
Calculating this:
\[ F = -75 \, \text{N} \]

### Step 4: Interpret the result
The negative sign indicates that the force exerted by the defender is in the opposite direction to the initial motion of the ball. Therefore, the average force exerted by the defender on the ball is:
\[ F = 75 \, \text{N} \, \text{(in the direction opposite to the ball's initial motion)} \]

### Final Answer
The average force exerted by the defender on the ball is **75 N**.

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