PLEASE HELP WILL UPVOTE:$)$ An m $=54\mathrm{.}0-$kg person running at an initial speed of v $=4\mathrm{.}10$ m$/$s jumps $($a$)$ Find the final velocity of the person and cart relative to the ground. $($Indicate the direction with the sign of your answer.$)$

onto an M $=108-$kg cart initially at rest $($figure below$).$ The person slides on the cart's top surface and finally comes to rest relative to the cart. The coefficient of kinetic friction between the person and the cart is $0\mathrm{.}380.$ Friction between the cart and ground can be ignored. $($Let the positive direction be to the right.$)$

A man of mass m is running on a raised platform at a speed v to the right. A cart of mass M$,$ which is on wheels, is on the ground just to the right of the platform, and the top horizontal surface of the cart is at the same height as the platform.

$($a$)$ Find the final velocity of the person and cart relative to the ground. $($Indicate the direction with the sign of your answer.$)$

m$/$s

$($b$)$ Find the friction force acting on the person while he is sliding across the top surface of the cart. $($Indicate the direction with the sign of your answer.$)$

N

$($c$)$ How long does the friction force act on the person?

s

$($d$)$ Find the change in momentum of the person. $($Indicate the direction with the sign of your answer.$)$

N $$ s

Find the change in momentum of the cart. $($Indicate the direction with the sign of your answer.$)$

N $$ s

$($e$)$ Determine the displacement of the person relative to the ground while he is sliding on the cart. $($Indicate the direction with the sign of your answer.$)$

m

$($f$)$ Determine the displacement of the cart relative to the ground while the person is sliding. $($Indicate the direction with the sign of your answer.$)$

m

$($g$)$ Find the change in kinetic energy of the person.

J

$($h$)$ Find the change in kinetic energy of the cart.

J