Finding the angle that maximizes height plus distance for a projectile

[rizzi143]

1. Consider a projectile, which is thrown at an angle of  with an initial velocity of v0.
 a) For a fixed angle, and the maximum height.
 b) Calculate the distance it travels before returning (gently, of course) to the
ground (which is assumed to be
flat).
 c) Use these pieces of information to and the angle which produces the maximum of the sum of height and distance.

 

[HallsofIvy]

This is a fairly typical homework problem so I am going to move this thread to the elementary physics homework area.

And, rizzi143, please show what you have tried yourself and where you are having problems.

If the initial speed (not velocity) is $v_0$ and the angle at which it is fired is $\theta$, do you know how to find the velocity vector? What are the vertical and horizontal components? Do you know what the acceleration vector looks like?