Question

a object is given a initial speed of 5.0 m/s up a 35 degrees incline. the mass of the object is 12.0 kg, and the coefficient of kinetic friction between the object and the incline is 0.15. how far up the incline does the object travel?

Answer 1

Start with the kinetic energy KE = (1/2) m v^2.

This is going to be expended in change of potential energy, m g h

and work done by friction, the force F' times the distance up the
incline. To get this force, you need the
normal force = weight cos(35)

and the friction force will equal (0.15) normal force.

loss of KE = increase in PE + (friction)(distance along incline)

Try to take this from here.