Football Player Kicking Ball: Find Clearance of Uprights

[hackett5]

Homework Statement

A football player has to kick a ball through the uprights that are 36m away and 3.05 high. He kicks the ball at 20m/s and at an angle of 53 degrees. By how much does the ball clear or fall short of the goal?

Homework Equations

Horizontal Range= v_i² sin 2$$\Theta$$/ g

Height = v_i²sin²$$\Theta$$/2g

The Attempt at a Solution

Using the formulas for range and hieght, I found that the ball traveled a total of 39.23m and reached a maximum height of 13.02. The ball traveled far enough, but how do I find how high the ball was at 36m to see if there was enough height?

 

[radou]

Hint: calculate the time at which the ball was at 36 m, and then plug that time into the equation that determines the height of the ball.