So I believe I figured out my error with the friction [needed to multiply by cos 45]. That still leaves me with 3.785 J of projectile work. If K=1/2 mv^2, then v=6.15 m/s launched at a 45 degree angle.
I just found the equation for range...R=2vx*vy/g. Came out to the correct answer of...
I see now I had an error with my potential energy. Height is 2m not 2.82m I like originally calculated. So at the top of the ramp, it still has 3.48 J of projectile motion. I don't know how to convert that to the velocity/acceleration to find the length d.
I think I have all the pieces here, and am able to solve for a work through the air. But I have a power output, and don't know how to isolate it to find the distance.
I just caught the cos/sin issue. And I wasn't sure about them being negative. Obviously they are, but I may be getting it confused. Class said g is just a scalar of 9.8 m/s^2, and we need to add in the signs so it would be +(-g). I just don't know when/where to add the negatives.
I believe the nx, Ty, and (fs)y are all 0. I could solve for theta if I could figure out (fs)x or ny.
edit: Track is frictionless, so delete (fs) forces.