Question

Calculate the impulse (in kgm/s) received by a football when it's kicked in a kickoff. The ball has a mass of 0.27 kg and travels a horizontal distance of 68 m. The ball is kicked at an angle q of 20.5 with the horizontal and spends 2.276 seconds in the air.

Answer 1

Vi is initial vertical velocity
u is horizontal velocity
S is initial speed

Do vertical problem first knowing it spends 2.276 s in air

That means it spends 1.138 seconds going up
v = Vi - g t
v = 0 at top
0 = Vi - 9.81 (1.138)
so
Vi = 11.16 meters/second

Answer 2

Is that enough?
remember tan 20.5 = Vi/u

Answer 3

so u = 29.8 meters/s
which you could also get from u = 68/2.276

Answer 4

S, initial speed = sqrt(u^2+v^2)

impulse = initial momentum
= .27 S

Answer 5

d = Xo*T = 68 m.
Xo * 2.276 = 68
Xo = 29.9 m/s. = Hor. component of
initial velocity.

Vo = Xo/cosA = 29.9/cos20.5 = 31.9 m/s =
Initial velocity.

Impulse = m*Vo = 0.27 * 31.9 = 8.61
kg.m/s.