How Do You Calculate Maximum Height and Range of a Projectile?

[ArmadylGS]

1) A projectile is launched with a speed of vo
at an angle of θo with respect to the horizontal. Derive an equation for the max height it reaches above its starting point in terms of g, θo, vo

I set Vox = vo and Voy = (V) sin θ, I tried everything and have no idea how the answer is H = (vo^2 sin^2 θ) / 2g

2) Calculate the angle of launch for an object so that maximum height of the object is equal to its horizontal range.
I worked with the formulas x = xo + vox*t + 1/2at^2 and y= yo + voy*t + 1/2at^2 and tried to set them equal to each other by solving for t on both sides. I did not know what to do after that.

Thanks

 

[rude man]

1)

I set Vox = vo and Voy = (V) sin θ, I tried everything and have no idea how the answer is H = (vo^2 sin^2 θ) / 2g

Why did you set Vox = vo? vo is the speed of the launched projectile at the angle θ.