Problem:

Lindsey's car is driving up a hill when her book bag, which she forgot on the roof, falls off. The bag has a mass of 19kg and slides up the hill 60 meters from its initial speed of 20m/s to rest. If the hill climbs at an angle of 30 degrees then what was the coefficient of friction?

My attempt:

Fn = 19*9.8cos30 = 161N

Vf^2 = Vi^2 + 2ad

0 = 202 + 2a(60)

-400 = 120a

a = -3.33 m/s2

F = ma

F = 19 * -3.33 = 63.27N

Ff = μmgcosx

63.27 = μ19*9.8*cos30

μ= .393

Is this correct? Is the parallel component required in this case? In what cases is it required?