Launch Angle for Maximum Field Goal Clearance

[RNelli22]

I need some help working the following problem. I have everything answered except #5 and that is where I get lost. Any help would be greatly appreciated.

Suppose a field goal kicker (American football) can kick the ball at a launch speed of 58 miles/hour. If the ball is placed at the 50-yard line, he is actually kicking the ball 60 yards to the goal post. Additionally, the crossbar is 10 feet above the ground. (1 mile = 5280 ft = 1760 yds = 1609.3 m)
1.Convert all distances to SI units; all answers will thus be in SI units.
2.Show that the ball easily clears the goal posts when kicked at the angle that produces maximum range.
3.For what kick angles will the ball clear the goal posts?
4.What is the closest a ball can land beyond the goal post for a made field goal?
5.What launch angle does the ball clear the goal post by the largest amount? How big is that amount?

 

[BiGyElLoWhAt]

hello RNelli, welcome to The forums of Physics.

Before I start throwing out suggestions, let me ask you a few things first, seeing as how you deleted the template.

I know you say you did 1-4, but would you mind showing what you got for them as well as how you got there?

Also, as far as 5 goes, I'm assuming your class is using kinematics (trig vs. calc based physics?)? If so what equations do you think would be useful in solving 5? If not we can go from there.

 

[SSWheels]

Find the formula for the height of the ball, in terms of the angle kicked (the only unknown).
Find the derivative of that formula and set equal to 0.
Solve for the angle.

Plugging that angle into the 2nd derivative should result in a negative number (a positive would indicate a minimum value, rather than a maximum value).

Without giving you the answer ... I came up with a value between 50 and 52 degrees.

You can calculate the clearance from there.