- #1
BarneyStinson
- 10
- 0
Homework Statement
Show that the range R can be expressed in terms of maximum height h, and in particular that R=4hcot[itex]\Theta[/itex]. Show that, when range is at a maximum, h=R/4
Homework Equations
R=(v(o)^2*2sin[itex]\Theta[/itex]cos[itex]\Theta[/itex])/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[itex]\Theta[/itex]
Plugged that into the first one:
R=(v(o)^2*2sin[itex]\Theta[/itex]cos[itex]\Theta[/itex])/g
R=(2gh*2sin[itex]\Theta[/itex]cos[itex]\Theta[/itex])/sin[itex]\Theta[/itex]g
Simplified to:
R=4hcos[itex]\Theta[/itex]
I don't know how to make it cot[itex]\Theta[/itex] 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.
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