A(n) 0.463 kg soccer ball approaches a player horizontally with a speed of 24.4 m/s. The player illegally strikes the ball with her hand
and causes it to move in the opposite direction with a speed of 16.2 m/s. What is the magnitude of the impulse delivered to the ball by the player? What are the steps to do this?
impulse is the change in momentum over time
To find the magnitude of the impulse delivered to the soccer ball by the player, you can use the impulse-momentum principle. The impulse is equal to the change in momentum of the ball. Here are the steps to calculate the impulse:
Step 1: Determine the initial momentum of the soccer ball.
The initial momentum (p) is calculated by multiplying the mass (m) of the soccer ball with its initial velocity (v). In this case, the mass of the soccer ball is given as 0.463 kg and the initial velocity is 24.4 m/s. So, the initial momentum can be calculated as follows:
p_initial = m * v_initial
Step 2: Determine the final momentum of the soccer ball.
The final momentum is calculated using the same formula but with the final velocity (v'). In this case, the final velocity is given as 16.2 m/s. So, the final momentum can be calculated as follows:
p_final = m * v_final
Step 3: Calculate the change in momentum.
The change in momentum (Δp) is the difference between the initial momentum and the final momentum. It can be calculated as follows:
Δp = p_final - p_initial
Step 4: Calculate the impulse.
The impulse (J) delivered to the soccer ball is equal to the change in momentum. So, the impulse can be calculated as follows:
J = Δp
Step 5: Find the magnitude of the impulse.
Since impulse is a vector quantity, the magnitude of the impulse is the absolute value of the impulse. So, the magnitude of the impulse can be calculated as follows:
|J| = |Δp|
By following these steps and plugging in the given values, you will be able to find the magnitude of the impulse delivered to the soccer ball by the player.