A soccer ball of mass 0.40 kg is rolling with velocity (0, 0, 1.8) m/s when you

Question

A soccer ball of mass 0.40 kg is rolling with velocity (0, 0, 1.8) m/s when you kick it. Your kick delivers an impulse of magnitude 1.6 N · s in the x direction. The net force on the rolling ball, due to the air and the grass, is 0.22 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.) I see a lot of people solving for the answer without using an iterative method, from what I've learned, that doesn't seem to be the correct method, but I also am not an expert.

Explanation / Answer

Impulse = (momentum after kick) - (momentum before kick)

Impulse= -1.6i

momentum before kick =0.4*1.8k

                                       = 0.72k

=> momentum after kick = -1.6i +0.72k

=> velocity after kick = -4i + 1.8k

net force due to grass and air =0.22 N

So, net deacceleration of ball=0.22/0.4

                                               = 0.55 m/sec2

velocity of ball after kick =sqrt(42 + 1.82)

                                       =4.38 m/sec

So, after 0.5 s position of ball =4.38*0.5 - 1/2*0.55*(0.5)2

                                                                =2.12 m   from origin

So, after 1 s position of ball =4.38*1 - 1/2*0.55*(1)2

                                                                =4.105 m   from origin

So, after 1.5 s position of ball =4.38*1.5 - 1/2*0.55*(1.5)2

                                                                =5.95 m   from origin

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