Question

A soccer ball player bounces the ball off her head, changing the velocity of the ball. She changes the x-component of the velocity of the ball from vix = 8.1 m/s to vfx = 4.7 m/s and the y-component from viy = −3.3 m/s to vfy = 3.2 m/s. If the ball has a mass of 0.44 kg and is in contact with the player's head for 7.1 ms, determine the following. (a) direction of the impulse (in degrees counterclockwise from the +x-axis) delivered to the ball ° counterclockwise from the +x-axis (b) magnitude of the impulse (in kg · m/s) delivered to the ball kg · m/s

Answer 1

The direction of the impulse delivered to the ball is approximately 34.3° counterclockwise from the +x-axis. The magnitude of the impulse delivered to the ball is approximately -1.496 kg·m/s.

Step-by-step explanation:

To determine the direction of the impulse delivered to the ball, we can use the formula:

θ = tan-1(vfy/vfx)

θ = tan-1(3.2/4.7)

θ ≈ 34.3° counterclockwise from the +x-axis

To find the magnitude of the impulse delivered to the ball, we can use the formula:

J = m(vfx - vix)

J = 0.44 kg(4.7 m/s - 8.1 m/s)

J ≈ -1.496 kg·m/s