A $62$ kg woman A sits atop the $76$ kg cart B$,$ both of which are initially at rest. It is given that $\backslash$theta $=26\backslash$deg and the woman slides down the incline of length L $=3\mathrm{.}5$ m$.$ Ignore the mass of the wheels on which the cart rolls and friction in their bearings, and neglect friction between the woman and the incline.

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

A person is sitting on the top sloped member of a truss$-$like structure on a horizontal cart.The person is labeled A$.$ The cart with the truss$-$like structure is labeled B$.$ The long sloped member, on which person A is sitting, from the left end of the cart is attached to the top end of the vertical member at the right end of the cart, making an angle theta with the horizontal. The other two vertical members are placed between the left and right ends of the cart separated by equal distances and supporting the long sloped member. The top end of the first vertical member from the left is attached through a sloped member to the bottom end of the second vertical member from the left. The top end of the second vertical member is attached through a sloped member to the bottom end of the third vertical member at the right end of the cart. The distance parallel to the long sloped member between the left end of the cart and person A is labeled L$.$

Determine the velocity of both the woman and the cart when she reaches the bottom of the incline. $($Round the final answers to four decimal places. Include a minus sign if necessary.$)$

The velocity of the woman is $(($

$)$ i$$

$+($

$)$ j$$

$)$ m$/$s$.$

The velocity of the cart is $($

i$$

$)$ m$/$s$.$