A tennis 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. Which statement is true concerning this situation?

Options

A. The momentum of the ball and the momentum of the earth both change.
B. Neither the momentum of the ball nor the momentum of the earth changes.
C. The momentum of the ball is changed, the momentum of the earth is not changed.
D. The momentum of the ball is unchanged, the momentum of the earth is changed.

Answer

To analyze the situation of the tennis ball bouncing off the ground, we can break down the problem step by step.

### Step 1: Identify the initial and final velocities
- The initial velocity of the tennis ball just before it strikes the ground is \( v_i = -12 \, \text{m/s} \) (downward direction is negative).
- The final velocity of the tennis ball after it bounces back is \( v_f = 12 \, \text{m/s} \) (upward direction is positive).

### Step 2: Calculate the initial and final momentum
- The momentum \( p \) of an object is given by the formula:
\[ p = m \cdot v \]
where \( m \) is the mass of the tennis ball and \( v \) is its velocity.
- Initial momentum \( p_i \):
\[ p_i = m \cdot v_i = m \cdot (-12) = -12m \, \text{kg m/s} \]
- Final momentum \( p_f \):
\[ p_f = m \cdot v_f = m \cdot 12 = 12m \, \text{kg m/s} \]

### Step 3: Calculate the change in momentum
- The change in momentum \( \Delta p \) is given by:
\[ \Delta p = p_f - p_i \]
Substituting the values:
\[ \Delta p = 12m - (-12m) = 12m + 12m = 24m \, \text{kg m/s} \]

### Step 4: Understand the implications of the change in momentum
- The change in momentum indicates that there is a net force acting on the ball during the collision with the ground.
- According to Newton's third law, the ground exerts an equal and opposite force on the ball.

### Step 5: Conclusion about the situation
- The statement that is true concerning this situation is that there is a change in momentum, and the forces involved during the collision are equal and opposite, affecting both the ball and the ground.