angle to maximize distance thrown

[minito6]

Supposed an object with initial speed v[sub:3jaforhr]0[/sub:3jaforhr] thrown at an initial angle ?. The height of the object at a given horizontal displacement x is given by (-16/v[sup:3jaforhr]2[/sup:3jaforhr][sub:3jaforhr]0[/sub:3jaforhr]cos[sup:3jaforhr]2[/sup:3jaforhr]?)x[sup:3jaforhr]2[/sup:3jaforhr] +tan (?)x. Find the angle that maximizes the distance thrown.

I drew a pic but don't know how to put it on here.
It shows a person, with an arc coming from the hand and going down. Also, from the hand, a straight line, right below the arc, which I called angle ?. I started by moving v[sup:3jaforhr]2[/sup:3jaforhr][sub:3jaforhr]0[/sub:3jaforhr] (cos[sup:3jaforhr]2[/sup:3jaforhr])? to the other side to get-

v[sup:3jaforhr]2[/sup:3jaforhr][sub:3jaforhr]0[/sub:3jaforhr](cos[sup:3jaforhr]2[/sup:3jaforhr])(?)=-16x[sup:3jaforhr]2[/sup:3jaforhr] + tan(?)x

Where do I go from here? That is, IF that's even correct.

 

[TchrWill]

Supposed an object with initial speed v[sub:1i662sqv]0[/sub:1i662sqv] thrown at an initial angle ?. The height of the object at a given horizontal displacement x is given by (-16/v[sup:1i662sqv]2[/sup:1i662sqv][sub:1i662sqv]0[/sub:1i662sqv]cos[sup:1i662sqv]2[/sup:1i662sqv]?)x[sup:1i662sqv]2[/sup:1i662sqv] +tan (?)x. Find the angle that maximizes the distance thrown.

I drew a pic but don't know how to put it on here.
It shows a person, with an arc coming from the hand and going down. Also, from the hand, a straight line, right below the arc, which I called angle ?. I started by moving v[sup:1i662sqv]2[/sup:1i662sqv][sub:1i662sqv]0[/sub:1i662sqv] (cos[sup:1i662sqv]2[/sup:1i662sqv])? to the other side to get-

v[sup:1i662sqv]2[/sup:1i662sqv][sub:1i662sqv]0[/sub:1i662sqv](cos[sup:1i662sqv]2[/sup:1i662sqv])(?)=-16x[sup:1i662sqv]2[/sup:1i662sqv] + tan(?)x

Where do I go from here? That is, IF that's even correct.

The horizontal distance traveled is given by d = (Vh^2/g)sin2? where Vh = the horizontal component of Vo, Vo(cos?) and g = 32 fps^2.

The farthest distance is reached when the angle ? is 45º, making sin(2?) = 1.0.