In a football match a ball is kicked by a player with a force of 25N for 0.2 sec and then by another player with a force of 70 N for 0.1 sec in the same direction. If the foot ball gains a velocity of 24 m/s after the two kicks, the mass of the foot ball is nearly

Options

A. 5 kg
B. 10 kg
C. 2.5 kg
D. 0.5 kg

Answer

To find the mass of the football, we can use the principle of momentum and the impulse-momentum theorem, which states that the change in momentum of an object is equal to the impulse applied to it.

### Step-by-Step Solution:

1. **Calculate the Impulse from the First Kick:**
- The impulse (change in momentum) from the first kick can be calculated using the formula:
\[ \text{Impulse} = \text{Force} \times \text{Time} \]
- For the first kick:
\[ \text{Impulse}_1 = 25 \, \text{N} \times 0.2 \, \text{s} = 5 \, \text{Ns} \]

2. **Calculate the Impulse from the Second Kick:**
- Similarly, for the second kick:
\[ \text{Impulse}_2 = 70 \, \text{N} \times 0.1 \, \text{s} = 7 \, \text{Ns} \]

3. **Calculate the Total Impulse:**
- The total impulse on the football is the sum of the impulses from both kicks:
\[ \text{Total Impulse} = \text{Impulse}_1 + \text{Impulse}_2 = 5 \, \text{Ns} + 7 \, \text{Ns} = 12 \, \text{Ns} \]

4. **Relate Impulse to Change in Momentum:**
- The total impulse is equal to the change in momentum of the football:
\[ \text{Total Impulse} = \Delta p = m \Delta v \]
- Here, \(\Delta v\) is the final velocity (24 m/s) since the ball starts from rest.

5. **Set Up the Equation:**
- We can rearrange the equation to solve for mass \(m\):
\[ 12 \, \text{Ns} = m \times 24 \, \text{m/s} \]

6. **Solve for Mass:**
- Rearranging gives:
\[ m = \frac{12 \, \text{Ns}}{24 \, \text{m/s}} = 0.5 \, \text{kg} \]

### Final Answer:
The mass of the football is approximately **0.5 kg**.