What Are the Optimal Kicking Angles for a Field Goal in Football?

[H2Owned]

Homework Statement

a football kicker can give the ball an initial speed of 25m/s. what are the least and greatest elevation angles at which he can kick the ball to score a field goal from a point 50m in font of the goalposts whose horizontal bar is 3.44 m above the ground.

Homework Equations

d = Vit + 0.5at^2

The Attempt at a Solution

Dx=distance in x direction
Dy=distance in y direction
and so on for Velocity and Acceleration

V = 25m/s
Dy = 3.44m
Vx = 25cos(theta)m/s
Vy = 25sin(theta)m/2
Ay = -9.8m/s^2

t = (Dx)/(Vx) = 50m/(25cos(theta))s

Now plug everything into an equation for Dy
Dy = Vy*t + 0.5Ay*t^2
3.44 = (25sin(theta))(2/cos(theta)) + 0.5(-9.8)(2/cos(theta))^2

I cannot get an answer for theta out of this equation..

The proper answers are 31 degrees and 63 degrees but i dot know how to solve it

 

[H2Owned]

nevermind i think i solved it. my calculator had a setting messed up somewhere that i couldn't find and kept giving me errors.

i reset my calculator and was able to solve it.