To calculate the impulse experienced by the ball when it hits the wall and rebounds, we can use the following formula for impulse:
\[ \text{Impulse} = \Delta p = p_{final} - p_{initial} \]
where \( p \) is the momentum, given by \( p = mv \).
Step 1: Calculate Initial Momentum
The initial momentum of the ball can be calculated using its mass and initial speed. Given that the mass \( m = 800 , \text{g} = 0.8 , \text{kg} \) (converting grams to kilograms) and the initial speed \( v_{initial} = 5 , \text{m/s} \):
\[ p_{initial} = m \cdot v_{initial} = 0.8 , \text{kg} \cdot 5 , \text{m/s} = 4 , \text{kg m/s} \]
Step 2: Calculate Final Momentum
After hitting the wall, the ball rebounds with the same speed but in the opposite direction. Therefore, the final velocity \( v_{final} = -5 , \text{m/s} \):
\[ p_{final} = m \cdot v_{final} = 0.8 , \text{kg} \cdot (-5) , \text{m/s} = -4 , \text{kg m/s} \]
Step 3: Calculate the Change in Momentum
Now we can calculate the impulse (change in momentum):
\[ \Delta p = p_{final} - p_{initial} = -4 , \text{kg m/s} - 4 , \text{kg m/s} = -8 , \text{kg m/s} \]
Step 4: Impulse
The impulse experienced by the ball is \( -8 , \text{kg m/s} \). The negative sign indicates that the impulse direction is opposite to the initial direction of the ball.
Thus, the magnitude of the impulse is:
\[ \text{Impulse} = 8 , \text{Ns} \]
Final Answer
The impulse experienced by the ball is \( 8 , \text{Ns} \).
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