Problem $1.$ A $40-$lb box is released down a smooth $($frictionless$)$ ramp with an initial velocity of $\backslash (3\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash ).$ At point $\backslash ($ B $\backslash )$ the box slides onto the surface of a cart. The coefficient of kinetic friction between the box and the cart is $0\mathrm{.}5$

A$.$ Determine the speed of the box at point B $,$ the bottom of the ramp.

B$.$ If the cart is prevented from moving, determine the distance $"\backslash ($ s $\backslash )"$ that the box slides on the cart before stopping..