Projectile motion from an angled slope

[BarneyStinson]

Homework Statement

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.)

Homework 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

The Attempt at a Solution

I drew a diagram of what is happening:

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 don't know where to plug 45 into.

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

Thanks.

 

[gneill]

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.