Question

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

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