Findi angular range given initial velocity and distance

[Niriz]

Homework Statement

A kicker is attempting a field goal from 50 m from the goal posts, which are 3.44 m high. He can kick the ball with initial speeds of 25 m/s. Ignoring air resistance, within what angular range must he kick the ball to score?

Homework Equations

Pf = Pi + Fnet*t
And any equations which can be derived from this (the kinematics formula)

The Attempt at a Solution

I've tried several approaches to this question but none of them seem to be able to neatly isolate one trigonometric function with a number. However I have come up with a few statements that I think should be true:

25m/s = (Vy^ + Vx^)^(1/2) since the components must equal 25 m,

And we know that Vy = sinθ*25 m/s while Vx = cosθ*25 m/s

The time it takes for the ball to reach the goalpost should equal 2/cosθ s, since it must travel 50 metres at a velocity of cosθ*25m/s.

For minimum angle I was thinking that, in time t, the vertical distance it travels must be 3.44 m, so I used the formula d = vi*t + (1/2)at^, so

3.44 m = sinθ*25*(2/cosθ) + 0.5(-9.8m/s^)(2/cosθ)^

But this does not turn simplify into a very nice formula... And is it right of me to think this? One of the biggest issues I'm having is not being able to produce a number for any velocity, because it could be any range of time or distance before Vfy = 0...

Any push in the right direction would be greatly appreciated! Such as another relationship equation...

 

[Niriz]

Someone brilliant please help me with this.. :P

 

[Niriz]

Also, the minimum angle should be at the point where the displacement vector of the ball is (50, 3.44, 0), since any more and the angle could be lower, and any less y displacement it wouldn't go over the post..

Bumping again!