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 = 7.9 m/s to vfx = 5.9 m/s and the y-component from viy = - 3.4 m/s to vfy = 4.5 m/s.

If the ball has a mass of 0.40 kg and is in contact with the player's head for 7.1 ms, determine the direction of the impulse (in degrees counterclockwise from the + x-axis) delivered to the ball.

change in momentum along x axis = mass (final velocity - initial velocity)

=.4 (5.9 - 7.9)

= -.8 kg m / s

change in momentum along y axis = mass (final velocity - initial velocity)

=.4 (4.5 + 3.4)

= 3.16 kg m/s

Force along x axis be Fx

Fx. t = change in momentum along x axis = -.8

Fy. t = change in momentum along y axis = 3.16

Direction of impulse =

Tanθ = Fy. t / Fx. t, θ is angle from x axis along anticlockwise direction.

= 3.16 / - 0.8.

= - 3.95

θ = 165.8 degree from positive x - axis. anticlockwise.