Verified answer

First of all, the best angle physically to kick/throw anything at is 45 degrees, not compensating for wind resistance and other outside factors. So it's kind of dumb for the punter to kick it at 79 degrees, but you can't blame him for being a jock... Anyway, we have a physics problem to answer!

The formula for position on the planet Earth in physics is always 1/2 x gt^2 + v(o)t + s(o). The O's in parentheses are bases/subscripts. G is gravity's pull downward on the ball, T is the amount of time the ball is in the air (which is what we are trying to find). V(o)t is the initial velocity times, once again, the time the ball is in the air. S(o) is the ball's starting height (in your problem, it is most likely assumed to be 0, although, realistically, it would be a few inches). Plug in your initial velocity to the formula, then find a quadratic equation for the degree measure of the ball's launch path by either using a calculator or computer application, then find the value for which T is greatest (i.e., the highest point on the curve in the graph).

Hopefully, this isn't too confusing, and if you're in a lower math than I am, I am sorry if I've applied properties you haven't yet learned! Perhaps your teacher/professor doesn't even want you doing it my way. Maybe you were taught how to do it differently...? It would help to know what math class you are in, but in any case, I hope you solve it correctly! Good luck:)