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

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 1.5 N · s in the x direction. The net force on the rolling ball, due to the air and the grass, is 0.28 N in the direction opposite to the direction of the ball's 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 pf/m. (Express your answer in vector form.) rf = Incorrect: Your answer is incorrect. m

I am supposed to do this problem with times steps of 0.5s until I get to 1.5s. If you could show each step in detail that would be most appreciated!!

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

-1.5 i = pf - m Vi

-1.5 i = pf - 0.5 (0i+0j+2k)

-1.5 i = pf - 1k

pf = -1.5 i + 1k

Vf= ( -1.5 i + 1 k ) / 0.5 = -3.0 i + 2 k

The average force on the ball is

Fav = J / t = 1.5 i / 0.5 = - 3.0 N

Net force on the ball is F = Fav- f = 3.0 N - 0.28N = 2.72N

Acceleration a = 2.72 N / 0.5 = 5.44m/s^2 along - x direction

a = -5.44 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)(-5.44 i+ 0 j+ 0k )

r = - 2.72 i + 0 j - 3k  

I hope help you.....

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