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 1.9

Answer #1

a)

F(t) = [8.5*10^4*t - 2.7*10^6*t^2]

Impulse = integral of F

So, Impulse = F(t)dt

So, Impulse = [8.5*10^4*t - 2.7*10^6*t^2]*dt = 8.5*10^4*t^2/2 - 2.7*10^6*t^3/3

So, for time t = 1.9*10^-3, Impulse = 8.5*10^4*(1.9*10^-3)^2/2 - 2.7*10^6*(1.9*10^-3)^3/3

So, Impuse = 0.147 kg.m/s <--------answer

b)

Average force = Impulse/time = 0.147/(1.9*10^-3 ) = 77.4 N <-----answer

c)

For maximum force, dF/dt = 0

So, 8.5*10^4 - 2.7*10^6*2*t = 0

So, t = 0.0157 s = 1.57*10^-2 s

d)

Impulse = mass*change of velocity

So, I = m*(vf - vi)

vi = 0

So, vf = I/m = 0.147/0.45 = 0.327 m/s <-----answer

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