A soccer ball of mass 0.43 kg is rolling with velocity (0,0,2.2) m/s, when you k

Question

A soccer ball of mass 0.43 kg is rolling with velocity (0,0,2.2) m/s, when you kick it. Your kick delivers an impulse of magnitude 1.3 Ns in the -x direction. The net force on the rolling ball, due to the air and the grass, is 0.25 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 v vector _avg approximately p vector f/m.

Explanation / Answer

making .use of the formula

we have p = mv------(1)

m = 0.43kg and v = 2.2m/s

substituting the values in eqn(1) we have

p = (0.43)(2.2)

p = 0.946kgm/s

the acceleration is given by

a = F / m----------(2)

taking Fnet = 0.25N AND SUBSTITUTING IN EQN (2) WE HAVE

a = 0.25 / 0.43 = 0.58m/s^2

we have the formula

v = u + at--------(3)

2.2 = u + (0.58)(1.5)

u = 1.33m/s

we have the formula to find the position of the ball as

v^2 = u^2 + 2as----------(4)

taking u = 0 in eqn (4)

(2.2)^2 = 0 + 2 (0.58)(s)

therefore the position s = 4.17m

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