Find the impulse experienced by a body.If the body mass `M` hits normally a rigid wall with velocity `v` and bounces back with the same speed.

Options

A. MV
B. 1.2 MV
C. 2 MV
D. Zero

Explanation

To find the impulse experienced by a body of mass \( M \) that hits a rigid wall with velocity \( v \) and bounces back with the same speed, we can follow these steps:

### Step 1: Understand the Initial and Final Momentum
When the body hits the wall, its initial momentum \( p_{\text{initial}} \) can be calculated as:
\[ p_{\text{initial}} = M \cdot v \]
where \( v \) is the velocity of the body before hitting the wall.

### Step 2: Calculate the Final Momentum
After bouncing back, the body moves in the opposite direction with the same speed. Thus, the final momentum \( p_{\text{final}} \) is:
\[ p_{\text{final}} = M \cdot (-v) = -M \cdot v \]
The negative sign indicates that the direction of the velocity has reversed.

### Step 3: Calculate the Change in Momentum
The impulse experienced by the body is equal to the change in momentum, which can be expressed as:
\[ \text{Impulse} = p_{\text{final}} - p_{\text{initial}} \]
Substituting the values from Step 1 and Step 2, we get:
\[ \text{Impulse} = (-M \cdot v) - (M \cdot v) \]
\[ \text{Impulse} = -M \cdot v - M \cdot v = -2M \cdot v \]

### Step 4: Interpret the Result
The impulse experienced by the body is \( -2M \cdot v \). The negative sign indicates that the impulse is in the opposite direction to the initial motion of the body.

### Final Answer
Thus, the impulse experienced by the body is:
\[ \text{Impulse} = 2M \cdot v \]