$(25$ points$)$ A spring is used to stop a $50-kg$ package that is moving down a $20$ incline. The spring has a constant $k=30\frac{N}{m}$ and is held by cables so that is initially compressed $50$ mm $.=0.$

Knowing that the velocity of the package is $2\frac{m}{s}$ when it is $8$ m from the spring and reglectines friction determine the maximum deformation of the spring in bringing the package to the rest.

$y$ axis wisht

$k=30\frac{N}{M}$

Work $=W_y$ dirtance

$W=m(g)$

$(50)\%8sin20$

Work $=1360605$

Yaxis

work done $67$ spring $0\mathrm{.}05$