How Does a Man Sliding on a Cart Affect Their Combined Speed and Energy?

[AznBoi]

I'm stuck on a lot of parts in this problem. I've been able to solve for some though. Any help is appreciated! =] Thanks!

Problem: A 60 kg man running at an initial speed of 4 m/s jumps onto a 120 kg cart initially at rest. He sildes on the cart's top surface and finally comes to rest relative to the cart. The coefficient of kinetic friction between the man and the cart is 0.400. Friction between the cart and ground can be neglected. a) Find the final speed of the man and cart relative to the ground. b) Find the frictional force acting on the man while he is sliding across the top surface of the cart. c) How long does the frictional force act on him? d) Find the change in momentum of the man and the change in momentum of the cart. e) Determine the displacement of the man relative to the ground while he is sliding on the cart. f) Determine the displacement of the cart relative to the ground while he is sliding. g) Find the change in the man's kinetic energy. h) Find the change in kinetic energy of the cart.

So far I have gotten:

b) Friction force= (mu)*(Normal force)
Ff=(0.4)(588N)
Ff=235N

a) How do you find the final speed of the man relative to the ground?? I don't get what it means by "relative to the ground" Would you use the
KE(initial)=KE(final) ?

I did it but I didn't get the right answer of 1.33m/s

.5(60)(4)^2=.5(180)(Velocity of combined masses)' ^2

and I got V=sqrt.(5.333) but that equals 2.31m/s

What am I doing wrong??

c) how do you find the time of the friction force that acts on him?? I know that he is travel rightwards initially at 4m/s and the friction acts opposite at 235N. What equation do I need to use to find the time until he stops? Is there a way to make 4m/s into a Force??

Thats all the help I need for now, thanks!

 

[Hootenanny]

For question (a), since the collision is inelastic one should use conservation of linear momentum.

For question (c), you should consider the impulse-momentum theorem