Projectile Motion - Incline Plane

[Harmony]

A person stands at the base of a hill that is a straight incline making an angle x with the horizontal. For a given initial speed v, at what angle y (to the horizontal) should objects be thrown so that the distance d they land up the hill is as large as possible?

I realize that tan x = vertical displacement/horizontal displacement, and d^2=horizontal distance^2+vertical distance^2. But no matter how do I manipulate the equation, it seems that I can't get rid of the variable t. Any help would be aprreciated.

 

[Dorothy Weglend]

You don't say enough about what you have done for me to figure out where you are in solving this problem.

The objects will follow a parabolic trajectory (I'm sure you know this). So perhaps starting with that would be a good first step.

Dorothy

 

[Hootenanny]

If you write your usual equations for your horizontal(d_x) and vertical(d_y) components in you should have something of the form;

$$d_{x}=v_{i}\cos(x)t$$

Do the same for your vertical component. You now have two functions of time. Also note that;

$$d_{x}=d\cos(y)$$

and

$$d_{y}=d\sin(y)$$

You should then equate the appropriate formulae and then manipulate your horizontal displacement into some of the form t=.... Can you go from here and figure out the last step yourself?