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 \( -10.64 , \text{kg m/s} \).