Football Player Kicking Ball: Find Clearance of Uprights

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A football player kicks a ball at 20 m/s and an angle of 53 degrees towards uprights 36 meters away and 3.05 meters high. The calculations show the ball travels a horizontal distance of 39.23 meters and reaches a maximum height of 13.02 meters. To determine if the ball clears the uprights, the time it takes to reach 36 meters must be calculated, and this time should be used to find the corresponding height of the ball. The discussion emphasizes the need to apply the projectile motion equations to assess the ball's clearance. Ultimately, the player needs to evaluate the height of the ball at the 36-meter mark to conclude if it clears the uprights.
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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= vi2 sin 2\Theta/ g

Height = vi2sin2\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?
 
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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.
 

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