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.

Explanation:

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.

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