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Projectile motion from an angled slope

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data

    A rock is thrown from the top of a slope that makes an angle of 30 degrees with the horizontal. At what angle to the horizontal should the rock be thrown to get a maximum range? (Hint: pick the direction of the slope as a new x axis and the normal to the slope as the new y axis. There will be acceleration in both axes.)

    2. Relevant equations

    y=y_o+v_y_o*-.5*g*t^2
    v_y=v_y_o+a_y*t

    x=x_o+v_x_o+.5a*t^2
    v_x=v_x_o

    3. The attempt at a solution

    I drew a diagram of what is happening:

    2wddod1.jpg

    I need to solve for theta.

    I don't think it will be 45 degrees to the horizontal, as you start on a slant. Even if i did think it was, i dont know where to plug 45 into.

    Can anyone guide me on the right path? Offer any more hints?

    Thanks.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 28, 2011 #2

    gneill

    User Avatar

    Staff: Mentor

    You'll have to write the equations of motion for the projectile in the given coordinate system and find an expression for the range (the x coordinate when the y coordinate reaches zero --- the projectile lands). The trick will be in maximizing this expression with respect to the launch angle. I think it would be easier to first solve for the angle with respect to the x-axis. It can always be adjusted to the horizontal reference afterwards.
     
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