What is the distance the block traveled before encountering the spring?

Question

A block starts from rest at the top of a 13.degree inclined plane and encounters a spring,of constant 4.5kN/m,rigidly attached to the plane.The blocks mass 64kg and it compresses the spring by 60cm.

Answer 1

Potential energy of the block equal to kinetic energy before encountering the string.
Kinetic energy of the block equal to energy of the spring compressed.

Pe=mgh
Ps=.5kx^2

mgh=.5kx^2
h=kx^2/(2mg)
h=[4.5 e+3 x (0 .6)^2]/[2 x 64 x 9.81)
h=1.2m
since in this cace
sin(13)=h/path
Path=h/sin(12)=
Path=1.2/sin(13)
Path=5.3 m