A crash test with simulated occupants for a new $2000$ lbf car model wants to measure the maximum speed that the shock absorber system protects the vehicle. It uses a lightweight barrier weighing $300$ lbf followed by a spring as shown in the foil. The spring has a coefficient of $700$ lbf$/$ft and a length of $22$ ft in its neutral state, finding that the car is protected while the spring is compressed a maximum of $12$ ft$.$ The coefficient of friction in the area before the barrier is $0\mathrm{.}8.$Assume that the vehicle is stationary at the end of the test and remains attached to the barrier $($box$)$ after impact.

$-$Enter the coefficient of restitution for this case

$-$enter the speed with which the block begins to move after impact

$-$Enter the speed before impact for the vehicle in Ft$/$s

$v_A=\frac{m}{s}$

$W_A=2000lbf$