So you chose to use a solid sphere and you give it a speed of 5.9m/s on a flat horizontal surface which is the speed it has when it reaches a 22degree incline. A) How far along the incline will it go?
I'm going to assume you're telling us it's a solid sphere that's rolling so we need to talk about KE and rotational KE...
1/2 m v^2 + 1/2I omega^2 = mgh
For a solid sphere (and don't ask me why I remember this) I = 2/5 mr^2
omega is v/r
so:
1/2 mv^2 + 1/5 mv^2 = mgh
h = 7/10 v^2 / g
Now do sin-1 to find the hypotenuse of the triangle.
If you haven't done rotational stuff yet, it's just 1/2mv^2 = mgh. Which is not really correct.