What Angle Maximizes Air Time for a 34.6m Football Punt?

AI Thread Summary
To maximize air time for a 34.6m football punt, the optimal angle from the horizontal is approximately 45 degrees, as this angle provides the longest airtime for a given range when neglecting air resistance. The calculations initially attempted yielded an angle of 29.0 degrees and a time of 1.98 seconds, which were deemed incorrect. The discussion highlights the importance of considering multiple solutions to the equations used, particularly the inverse sine function, which may only provide the principal value. Additionally, the possibility of punting at 90 degrees is mentioned, suggesting that this angle would maximize airtime but not achieve the desired range. Accurate calculations and consideration of all possible angles are crucial for solving the problem correctly.
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Homework Statement


A football punter can punt a maximum range of 40.8 m. If he instead wants to punt only 34.6 m, but maximize the time the ball is in the air, at what angle from the horizontal should he kick the ball, and how long will it stay in the air if he hits it perfectly? (neglect air resistance) Assume he can kick the ball with the same force every time.

Homework Equations


  • R = (u2sin 2θ) / g
  • Rmax = u2/g

The Attempt at a Solution



I used the above equations to solve the problem but I'm getting 29.0 degrees and 1.98 seconds. When I try to submit my answers says it's wrong. Do I have the right sig figures or it just something wrong on my calculations
 
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Hello and welcome to PF!

Consider the possibility that there might be more than one mathematical solution to your equations. In particular, the inverse sine function on your calculator probably only gives you the "principal value". For example, my calculator tells me sin-1(0.5) is 30 degrees. It misses the fact that sin(150o) is also 0.5.
 
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Why don't you show your calcs.

What if he kicked it at 90 degrees?
 
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