A spring $($k $=220$ N$/$m$)$ is fixed at the top of a frictionless plane inclined at angle $0=38.$ A $1\mathrm{.}7$ kg block is

projected up the plane, from an initial position that is distance d $=0\mathrm{.}70$ m from the end of the relaxed

spring, with an initial kinetic energy of $32$ J$.($a$)$ What is the kinetic energy of the block at the instant it

has compressed the spring $0\mathrm{.}20$ m$?($b$)$ With what kinetic energy must the block be projected up the

plane if it is to stop momentarily when it has compressed the spring by $0\mathrm{.}50$ m$?$

e