A 1 kg ball has a velocity of 12 m/s downward just before it strikes the ground and bounces up with a velocity of 12 m/s upward. What is the change in momentum of the ball?

Options

A. zero kg m/s
B. 12 kg m/s, downward
C. 12 kg m/s, upward
D. 24 kg m/s, upward

Answer

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

### Step 1: Identify the mass and velocities
The mass of the ball (m) is given as 1 kg. The initial velocity (u) just before it strikes the ground is 12 m/s downward, and the final velocity (V) after it bounces back is 12 m/s upward.

### Step 2: Define the direction of velocities
We need to define the direction of the velocities. We can consider upward as positive and downward as negative. Therefore:
- Initial velocity (u) = -12 m/s (downward)
- Final velocity (V) = +12 m/s (upward)

### Step 3: Calculate the initial momentum
The initial momentum (p_initial) of the ball can be calculated using the formula:
\[ p_{initial} = m \cdot u \]
Substituting the values:
\[ p_{initial} = 1 \, \text{kg} \cdot (-12 \, \text{m/s}) = -12 \, \text{kg m/s} \]

### Step 4: Calculate the final momentum
The final momentum (p_final) of the ball can be calculated using the formula:
\[ p_{final} = m \cdot V \]
Substituting the values:
\[ p_{final} = 1 \, \text{kg} \cdot (12 \, \text{m/s}) = 12 \, \text{kg m/s} \]

### Step 5: Calculate the change in momentum
The change in momentum (Δp) is given by the difference between the final momentum and the initial momentum:
\[ \Delta p = p_{final} - p_{initial} \]
Substituting the values:
\[ \Delta p = 12 \, \text{kg m/s} - (-12 \, \text{kg m/s}) \]
\[ \Delta p = 12 \, \text{kg m/s} + 12 \, \text{kg m/s} \]
\[ \Delta p = 24 \, \text{kg m/s} \]

### Conclusion
The change in momentum of the ball is **24 kg m/s** upward.

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