I deriving equtions for projectile motion.

[BarneyStinson]

Homework Statement

Show that the range R can be expressed in terms of maximum height h, and in particular that R=4hcot$\Theta$. Show that, when range is at a maximum, h=R/4

Homework Equations

R=(v(o)^2*2sin$\Theta$cos$\Theta$)/g
v(y)^2=v(yo)^2-2gh

The Attempt at a Solution

I used the second equation to find a value for v(o)^2 to substitute into the first equation. I got:

v(o)^2=2gh/sin$\Theta$

Plugged that into the first one:

R=(v(o)^2*2sin$\Theta$cos$\Theta$)/g
R=(2gh*2sin$\Theta$cos$\Theta$)/sin$\Theta$g

Simplified to:

R=4hcos$\Theta$

I don't know how to make it cot$\Theta$ instead of cos. Maybe i used the wrong equations or something.

For (b), I drew the flight path, dividing the range into 4 equal parts, then showed that the height is equal to one of the quarters of the range. I need to show it mathematically, any hints on that?

Thank you guys for any help.

 

[BarneyStinson]

Ok, i found it. I used the wrong equation for height.

This is the right one: http://upload.wikimedia.org/math/9/7/e/97e83759703c5fa053baed5f06c1dfa7.png

I still don't understand the second part though.

 

[BarneyStinson]

Since my teacher never gave us the equation for height i posted above, he said we have to derive it ourselves... I have no idea how to do this, can you guys help me out?

And i still don't understand how to derive the equation R=h/4