A bull of mass m is moving towards a player with velocity v. If player stopped it, then impulse applied by the player is

Options

A. `-mv`
B. `+mv`
C. `-2mv`
D. `+2mv`

Answer

To solve the problem of finding the impulse applied by the player to stop a ball of mass \( m \) moving with velocity \( v \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial Momentum**:
The initial momentum \( p_i \) of the ball can be calculated using the formula:
\[ p_i = m \cdot v \]
where \( m \) is the mass of the ball and \( v \) is its initial velocity.

2. **Identify the Final Momentum**:
When the player stops the ball, its final velocity \( v' \) becomes 0. Therefore, the final momentum \( p_f \) is:
\[ p_f = m \cdot 0 = 0 \]

3. **Calculate the Change in Momentum**:
The change in momentum \( \Delta p \) is given by the difference between the final momentum and the initial momentum:
\[ \Delta p = p_f - p_i = 0 - (m \cdot v) = -m \cdot v \]

4. **Relate Change in Momentum to Impulse**:
According to the impulse-momentum theorem, impulse \( J \) is equal to the change in momentum:
\[ J = \Delta p \]
Therefore, substituting the change in momentum we calculated:
\[ J = -m \cdot v \]

5. **Interpret the Result**:
The negative sign indicates that the impulse is in the opposite direction to the motion of the ball, which makes sense since the player is stopping the ball.

### Final Answer:
The impulse applied by the player to stop the ball is:
\[ J = -m \cdot v \]