Projectile motion - have i done this correctly?

[Mglafas]

I'm unsure whether I have done the following problem correctly :)

Homework Statement

A ball is kicked at from the slope as shown.
When will the ball hit the slope?

http://img90.imageshack.us/img90/8084/slopevi0.th.jpg

Homework Equations

The distance traveled can be expressed in two components:
Sx=vt
Sy=0.5gt^2

The displacement compontents can also be expressed in terms of tan(a)
tan(a)=Sy/Sx

The Attempt at a Solution

Substituting we get:
Sy=Sx*tan(a)
0.5gt^2=vt*tan(a)
0.5gt=v*tan(a)
t=[2v*tan(a)]/g

Is this correct?

 

[mezarashi]

Your approach is looks sound to me. The idea is you want to find the components x and y that match the slope of the ramp.

 

[LowlyPion]

Substituting we get:
Sy=Sx*tan(a)
0.5gt^2=vt*tan(a)
0.5gt=v*tan(a)
t=[2v*tan(a)]/g

Is this correct?

That looks fine.

What you apparently developed is the equation for angle of the ball, as a function of t, from some point down the slope, and by setting the angle of tan to θ, that's where it hits and you have the value for the time now as a function of V_o and θ. Good job.