Question

A 0.14 kg baseball is thrown horizontally at 38. m/s and after it is struck by a bat, it travels at -38. m/s. What impulse did the bat deliver to the ball?

Answer 1

To calculate the impulse delivered to the baseball by the bat, we can use the formula for impulse:

\[
\text{Impulse} = \Delta p = p_f - p_i
\]

where \( p_f \) is the final momentum and \( p_i \) is the initial momentum of the baseball.

First, we need to calculate the initial momentum \( p_i \) and the final momentum \( p_f \). Momentum is given by the formula:

\[
p = m \cdot v
\]

where \( m \) is the mass and \( v \) is the velocity.

### Step 1: Calculate initial momentum \( p_i \)

The initial velocity \( v_i \) is \( 38 \, \text{m/s} \) (positive because it's in the positive horizontal direction):
\[
p_i = m \cdot v_i = 0.14 \, \text{kg} \cdot 38 \, \text{m/s} = 5.32 \, \text{kg m/s}
\]

### Step 2: Calculate final momentum \( p_f \)

The final velocity \( v_f \) is \( -38 \, \text{m/s} \) (negative because it's in the opposite direction):
\[
p_f = m \cdot v_f = 0.14 \, \text{kg} \cdot (-38 \, \text{m/s}) = -5.32 \, \text{kg m/s}
\]

### Step 3: Calculate change in momentum

Now we can find the impulse:
\[
\Delta p = p_f - p_i = (-5.32 \, \text{kg m/s}) - (5.32 \, \text{kg m/s}) = -10.64 \, \text{kg m/s}
\]

The negative sign indicates that the impulse was in the opposite direction of the initial momentum of the baseball.

### Conclusion

The impulse delivered to the ball by the bat is \( -10.64 \, \text{kg m/s} \).