A soccer player kicks a soccer ball of mass 0.45 kg that is initially at rest. T

Question

A soccer player kicks a soccer ball of mass 0.45 kg that is initially at rest. The player's foot is in contact with the ball for 2.0 10-3 s. The force of the kick is given by
F(t) = [(7.1 106)t - (2.2 109)t2] N,
for 0 t 2.0 10-3 s, where t is in seconds.
(a) Find the magnitude of the impulse imparted to the ball.
___ N·s
(b) Find the magnitude of the average force exerted by the player's foot on the ball during the period of contact.
___ N
(c) Find the magnitude of the maximum force exerted by the player's foot on the ball during the period of contact.
___ N
(d) Find the magnitude of the ball's velocity immediately after it loses contact with the player's foot.
___ m/s

Explanation / Answer

a) Impulse = F.dt = 7.1*10^6 t^2 / 2 -2.2 *10^9 t^3/3 = 8.333 b) average force = impulse / time = 8.333 / (2*10^-3) = 4166.66 N c) max force = df /dt = 0 max f = 5728.409N d) mv = impulse = 8.333 v = 18.518 m/sec

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