A 0.40 kg soccer ball approaches a player horizontally with a velocity of
18 m/s to the north. The player strikes the ball and causes it to move in the opposite direction with a velocity of 22 m/s. What impulse was delivered to the ball by the player?
To find the impulse delivered to the ball by the player, we can use the impulse-momentum theorem, which states that the impulse is equal to the change in momentum:
Impulse = Change in momentum
First, we need to calculate the momentum of the ball before and after the player strikes it.
Initial momentum of the ball (before the player strikes it):
Mass = 0.40 kg
Velocity = 18 m/s (to the north)
Initial momentum = Mass x Velocity = 0.40 kg x 18 m/s = 7.2 kg.m/s (to the north)
Final momentum of the ball (after the player strikes it):
Mass = 0.40 kg
Velocity = -22 m/s (to the south, opposite direction)
Final momentum = Mass x Velocity = 0.40 kg x (-22 m/s) = -8.8 kg.m/s (to the south)
Now, calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = (-8.8 kg.m/s) - (7.2 kg.m/s)
Change in momentum = -8.8 kg.m/s - 7.2 kg.m/s
Change in momentum = -16 kg.m/s
Therefore, the impulse delivered to the ball by the player is 16 kg.m/s.