Your answer is partially correct. Try again. A soccer player kicks a soccer ball

Question

Your answer is partially correct. Try again. 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 1.4 x 10-3 s, and the force of the kick is given by F(t) = [(7.8 x 105)t - (2.0 x 108)t2] N for 0 t 1.4 x 10-3 s, where t is in seconds. Find the magnitudes of the following: (a) the impulse on the ball due to the kick, (b) the average force on the ball from the player's foot during the period of contact, (c) the maximum force on the ball from the player's foot during the period of contact, and (d) the ball's speed immediately after it loses contact with the player's foot.

Explanation / Answer

mass=m=0.45 kg

time of contact=t=1.4 ms

F=7.8*10^5*t - 2*10^8*t^2

a)impulse=integral of F*dt

=0.5814 N.s

b)average force=impulse/time of contact=415.33 N

c)for maimum force,

dF/dt=0

7.8*10^5=4*10^8*t

t=1.95 ms

so force=760.5 N

d)balls speed=impuse applied/mass=1.292 m/s

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