A soccer ball of mass 0.30 kg is rolling with velocity 0, 0, 2.6 m/s, when you kick it. your kick delivers an impulse of magnitude

Question

Donna Lang

Physics

12 October, 01:12

A soccer ball of mass 0.30 kg is rolling with velocity 0, 0, 2.6 m/s, when you kick it. your kick delivers an impulse of magnitude

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Alberto Holder · Answer 1

Vo = I/m = 1.4 N*sec/0.75 kg = 1.866 m/sec

Eo = m/2*Vo^2 = 1.866^2*0.375 = 2.61 joule

after 2 meters

E1 = Eo-0.20*2 = 2.61-0.4 = 2.21 joule

V1 = Vo*√E1/Eo = 1.866*√2.21/2.61 = 1.717 m/sec

2*2 = (1.866+1.717) * t

t1 = 2*2 / (1.866+1.717) = 1.116 sec

a1 = - (1.866-1.717) / 1.116 = - 0.134 m/sec^2

after 4 meters

E2 = Eo-0.20*4 = 2.61-0.8 = 1.81 joule

V2 = Vo*√E2/Eo = 1.866*√1.81/2.61 = 1.554 m/sec

t2 = 2*2 / (1.717+1.554) = 1.223 sec

a2 = - (1.717-1.554) / 1.223 = - 0.133 m/sec^2

a = (a1+a2) / 2 = - 0.1335 m/sec^2

d (t) = Vo*t+a/2*t^2

after 1,5 sec:

d = 1.866*1.5-0.1335/2*2.25 = 2.65 m