A quarterback throws a spiral to a receiver that is 40m away. The football has a spin of 14 rev/s and went through 58 revolutions before being caught. if the ball is caught at the same height it was thrown at, at what velocity and at what angle should the quarterback throw the ball?

Answer 1

time in air: 58/14 seconds.

distance=vi*cosTheta*t
40=vi*cosTheta*58/14

time in air:
hf=hi+vi*sinTheta*t-1/2 g t^2
0=0+vi*sinTheta*58/14-4.9(58/14)^2

so now, two equations. solve for v in the upperone.
vi=40*14/58*1/cosTheta

put that in the second equation
40*14/58*tanTheta*58/14 -4.9(58/14)^2
solve for tan theta, then theta. Now with theta, you can solve vi.