A soccer ball of mass 0.50 kg is rolling with velocity (0, 0, 2.0) m/s, when you

Question

A soccer ball of mass 0.50 kg is rolling with velocity (0, 0, 2.0) m/s, when you kick it. Your kick delivers an impulse of magnitude 1.2 N s in the -x direction. The net force on the rolling ball, due to the air and the grass, is 0.21 N in the direction opposite to the direction of the balls momentum. Using a time step of 0.5 s, find the position of the ball at a time 1.5 s after you kick it, assuming that the ball is at the origin at the moment it is kicked. Use the approximation Vavg approx pf/m. (Express your answer in vector form.) rf= m

Explanation / Answer

The initial speed of the ball Vi = (0i + 0j + 0 k)

Final speed of the ball Vf = (0i + 0j + 2 k)

Impulse on the ball is equal to change in momentum of the ball

J = pf - pi

-1.2 i = pf - m Vi

-1.2 i = pf - 0.5 (0i+0j+2k)

-1.2 i = pf - 1k

pf = -1.2 i + 1k

Vf= ( -1.2 i + 1 k ) / 0.5 = -2.4 i + 2 k

The average force on the ball is

Fav = J / t = 1.2 i / 0.5 = - 2.4 N

Net force on the ball is F = Fav- f = 2.4 N - 0.21N = 2.19N

Acceleration a = 2.19 N / 0.5 = 4.38m/s^2 along - x direction

a = -4.38 i +0 j+0 k

The position of the ball after 1.5s

r = Vi.t + (1/2) a t ^2

r = (0i+0j+2k) (1.5) +(1/2)(-4.38 i+ 0 j+ 0k )

r = - 2.19 i + 0 j - 3k

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