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 = 9.5 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 delivered to the ball ° counterclockwise from the +x-axis b) magnitude of the impulse delivered to the ball

Answer 1

the formula for impulse is

J = change in momentum

J = m (vf- vi)

change in speed in x direction vx= 4.7 -9.5 =   -4.8 m/s

change in speed in y direction vy= 3.2- (-3.3) =   + 6.5 m/s

direction of impulse is

       tanθ = 6.5 / 4.8

θ = 53.55 deg above the -x axis, which is   

180 -53.55 =   126.44 deg from the +x axis

magnitude of Δv = root(4.8² + 6.5² ) = 8.08m/s

magnitude of impulse J = m Δv = 0.44 * 8.08 =3.55 kg-m/s