A football player kicks a 0.25 kg ball and imparts it a velocity of 10 m/s. The contact between foot and the ball is only `(1)/(50)th` of a second. The kicking force is

Options

A. 250 N
B. 125 N
C. 0 N
D. 3.78 N

Answer

To find the kicking force applied by the football player on the ball, we can use Newton's second law, which states that force is equal to the change in momentum per unit time. Here’s how we can solve the problem step by step:

### Step 1: Understand the Problem
We need to calculate the force exerted on a 0.25 kg football that is kicked to achieve a velocity of 10 m/s. The contact time between the foot and the ball is \( \frac{1}{50} \) seconds.

### 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:
- \( m \) = mass of the ball = 0.25 kg
- \( v_f \) = final velocity = 10 m/s
- \( v_i \) = initial velocity = 0 m/s (the ball is at rest before being kicked)

Substituting the values:
\[ \Delta p = 0.25 \, \text{kg} \cdot (10 \, \text{m/s} - 0 \, \text{m/s}) = 0.25 \, \text{kg} \cdot 10 \, \text{m/s} = 2.5 \, \text{kg m/s} \]

### Step 3: Calculate the Force
According to Newton's second law, the force (\( F \)) can be calculated using the formula:
\[ F = \frac{\Delta p}{\Delta t} \]
where:
- \( \Delta t \) = time of contact = \( \frac{1}{50} \) seconds

Substituting the values:
\[ F = \frac{2.5 \, \text{kg m/s}}{\frac{1}{50} \, \text{s}} = 2.5 \, \text{kg m/s} \cdot 50 \, \text{s}^{-1} \]
\[ F = 125 \, \text{N} \]

### Conclusion
The kicking force applied by the football player on the ball is **125 Newtons**.

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