Horizontal path of a baseball as a sine function

[Jacobpm64]

A baseball hit at an angle of a to the horizontal with initial velocity v₀ has horizontal range, R, given by

R = (v₀² / g)sin(2a)

Here g is the acceleration due to gravity. Sketch R as a function of a for 0 < a < pi/2. What angle gives the maximum range? What is the maximum range?

For the graph, would I just graph a sin curve where the maxes are at v₀²/g and the mins are at -v₀²/g... And of course I'd keep the domain restricted as the question said. Then it would have a period of pi as well, and that would be enough info to graph it out right?

As for the angle that gives the maximum range, I'd probably have to use the graph and divide one oscillation into parts to see where in that interval the maximum was reached.

And, for the last question, I guess the maximum would be v₀²/g?

Just tell me if my reasoning is correct.

Thanks

 

[xman]

First, this question is more a physics question than a math question. Second, you could differentiate wrt a and solve, or just remember what value of the argument is the sine function maximum, then divide this by two. Other than that you have the right idea.