Problem $3$

Consider the situation depicted in Figure $2$: A box of mass $m=\mathrm{.}250kg$ slides down a frictionless rollercoaster. The total energy of the box is measured to be $E=100J$ as it slides down the first incline. If $v_a=10\frac{(m)}{(s)}$ determine a$)$ the initial height, $h,$ of the box. Also, determine the velocities b$)v_B$ and c$)v_c$ of the box. $($Note: The initial energy of the system is taken with respect to a co$-$ordinate system with origin placed at ground level.$)$

If at the end of the boxes journey it comes to a complete STOP by slamming into a spring with springconstant $k=100Nm,d$ determine the amount the spring was compressed from it's equilibrium value, $x.($Note: The height of the box when it comes to a stop against the spring is $\frac{3}{5}h.)$

Figure $1$