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 v_ix = 9.9 m/s to v_fx = 4.6 m/s and the y-component from v_iy =

−3.4

m/s to v_fy = 5.4 m/s. If the ball has a mass of 0.41 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

Impulse is equal to change in momentum. We use this to find the required direction and magnitude of impulse as shown below

impulse - Ap So, AP ac = m m ("fx- Vise) n (0.4119) (4.6 m/s - 9.9015) = -2 173 legomis APY 17 m (Ufy - Viy) -0.4119) 5.4 ms -1-3-4m/s)) = 3.608 kg.m/s tano = .Y APYL 3.608 2.173 Apy APx) APx o = 58.94 So, direction . 180-0 = 180° - 58.94 0 = 121.06 b) Apl SUAP ²+ ((Apyl) ² SE2.173)2 + (3.608)2 - = 4.21 kg. m/s