Question

A projectile is fired with a velocity u at right angles to the slope, which is inclined at an angle theta with the horizontal. Derive and expression for the distance R to the point of impact.


The only think I know to do in this situation is to make the x-axis parallel and y-axis perpendicular to the incline. I have no idea what to do after that

Answer 1

The horizontal velocity component is U sin theta. The vertical component is U cos theta.

The height of the projectile from the launch point is
Y = U cos theta t - (g/2) t^2
The horizontal displacement from the launch point is
X = -U sin theta * t
The point of impact is where
Y = -R cos theta, and
X = -R sin theta

Knowing that Y/X = tan theta should let you solve for t, and then evaluate R, but it is a messy process.

Answer 2

projectile