A ball of mass `0*2` kg moving with a speed of 30 m/s strikes a bat returns in opposite direction with speed of 90m/s . Magnitude of change in momentu,m of ball will be

Options

A. Zero
B. 6 kg m/s
C. 12 kg m/s
D. 24 kg m/s

Answer

To find the magnitude of the change in momentum of the ball, we can follow these steps:

### Step 1: Identify the mass and velocities
- Mass of the ball, \( m = 0.2 \, \text{kg} \)
- Initial velocity of the ball before striking the bat, \( v_1 = 30 \, \text{m/s} \) (in the positive direction)
- Final velocity of the ball after striking the bat, \( v_2 = -90 \, \text{m/s} \) (in the opposite direction, hence negative)

### Step 2: Calculate the initial momentum
The initial momentum (\( p_i \)) of the ball can be calculated using the formula:
\[ p_i = m \cdot v_1 \]
Substituting the values:
\[ p_i = 0.2 \, \text{kg} \cdot 30 \, \text{m/s} = 6 \, \text{kg m/s} \]

### Step 3: Calculate the final momentum
The final momentum (\( p_f \)) of the ball after it strikes the bat can be calculated as:
\[ p_f = m \cdot v_2 \]
Substituting the values:
\[ p_f = 0.2 \, \text{kg} \cdot (-90 \, \text{m/s}) = -18 \, \text{kg m/s} \]

### Step 4: Calculate the change in momentum
The change in momentum (\( \Delta p \)) is given by:
\[ \Delta p = p_f - p_i \]
Substituting the values:
\[ \Delta p = -18 \, \text{kg m/s} - 6 \, \text{kg m/s} = -24 \, \text{kg m/s} \]

### Step 5: Find the magnitude of the change in momentum
The magnitude of the change in momentum is:
\[ |\Delta p| = 24 \, \text{kg m/s} \]

### Final Answer:
The magnitude of the change in momentum of the ball is \( 24 \, \text{kg m/s} \).

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