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I need help deriving equtions for projectile motion.

  1. Sep 26, 2011 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations

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

    3. 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.
     
    Last edited: Sep 26, 2011
  2. jcsd
  3. Sep 26, 2011 #2
  4. Sep 27, 2011 #3
    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 dont understand how to derive the equation R=h/4
     
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