In a circus performance, a monkey on a sled

Question

is given an initial speed of 3.9 m/s up a 17
◦
incline. The combined mass of the monkey
and the sled is 18.1 kg, and the coefficient
of kinetic friction between the sled and the
incline is 0.34.
The acceleration of gravity is 9.81 m/s
2
.
How far up the incline does the sled move?
Answer in units of m

Answer 1

Use conservation of energy

(Increase in potential energy) = (Initial kinetic energy) + (work done against friction)

Let L be the length it goes up the incline.
M*g*L*sin 17 = (1/2)*MVo^2 + M*g*L*cos17*(mu_k)

mu_k is the kinetic friction coefficient, 0.34

Cancel out the M's and solve for L