Projectile motion - have i done this correctly?

AI Thread Summary
The discussion focuses on solving a projectile motion problem involving a ball kicked from a slope. The user expresses uncertainty about their calculations, specifically regarding the time it takes for the ball to hit the slope. They derive equations for the horizontal and vertical components of motion, ultimately arriving at a formula for time based on initial velocity and angle. Responses confirm that the approach and calculations are correct, validating the user's method. The solution effectively relates the ball's trajectory to the slope's angle, providing a clear understanding of the problem.
Mglafas
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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?
 
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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.
 
Mglafas said:
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 Vo and θ. Good job.
 
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