Tough physics problem!?

Question

If you could show your work, that would be great!
A football punter wants to kick the ball so that it hits the ground 50 meters from where it is kicked and so that the ball is in the air 4 seconds. At what angle and with what initial speed should the ball be kicked? Assume that the ball leaves the kicker's foot from and elevation of 1 meter.

Answer 1

The equations of motion for the ball are
y(t)=1+v0*sin(θ)*t-.5*g*t^2
x(t)=v0*cos(θ)*t

when y(4)=0 and x(4)=50, we have impact at the desired spot with the desired hang time

0=1+v0*sin(θ)*4-9.81*8
v0*sin(θ)=19.37
v0*cos(θ)=12.5
divide the two equations
tan(θ)=19.37/12.5
θ=57.16 degrees

now solve for v0
23.05 m/s

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