Football kicked 52 yards horizontally to a goal 10 ft high

[cellfoneguy]

Homework Statement

A football is kicked towards a goal (The little fork thingies, whetever they're called) 10 ft high. The horizontal distance is 52 yards. The initial velocity is 55 mph. Find all angles you can kick the ball at so that it goes over the goal.

Homework Equations

The kinematics equations
d=vit+(at^2)/2
d=(vi+vf)*t/2
Vf=Vi+at
Vf^2=Vi^2+2ad
f=ma
d=vt

The Attempt at a Solution

55 mph is 242/3 ft/s.
so i drew the triangle, with a horizontal length of 156 ft. The height is 10ft. I know i need to find the height in terms of theta.
I split this problem into the x and y directions.
for x, i know vf and vi are both cos(theta)242/3
d=156.
I used d=(vi+vf)*t/2.
it's basically d=cos(theta)242/3 * t
so i foudn that t=1.938/cos(theta)
and then I'm stuck. what do i do after that?

 

[AtticusFinch]

Ok so you have,

$$t=\frac{1.938}{cos(\theta)}$$

in the x direction.

You also know in the y-direction,

$$\Delta y = \frac{243}{3}sin(\theta) t - \frac{1}{2} g t^2$$

You know what $$\Delta y$$ is so substitute the two equations and solve for possible values of theta.