Ignore part A. I can\'t figure out part B 16. A cart of mass M is approaching a
ID: 1792793 • Letter: I
Question
Ignore part A. I can't figure out part B
16. A cart of mass M is approaching a platform at a speed relative to the ground. A person of mass m sees the cart coming and wants to jump onto the cart, as shown in Figure 9. He jumps toward the cart at a horizontal speed u relative to the ground. Ignore the effects of rolling friction, and assume that the axles spinning the wheels on the cart are very well lubricated Figure 9: A person jumping at a horizontal speed u off of a platform and onto a cart moving toward the man at a speed o. (a) Find the velocity of the person-cart system when he lands on the cart and comes to rest relative to the cart b) Upon coming to rest relative to the cart, say, near the right side of the cart, the person decides that he wants to jump rightward off of the cart. Suppose he jumps off in such a way that his horizontal speed relative to the cart after jumping off is, again, u. i. Determine the velocity of the CM of the cart-person system after he jumps off of the cart ii. Determine the velocity of the person relative to the ground after he jumps off of the cart. iii. Determine the velocity of the cart relative to the ground after he jumps off of the cart.Explanation / Answer
i] velocity of center of mass will be conserved in horizontal direction.
vf*(M+m) = Mv - mu
vf = [Mv - mu]/(M+m)
ii] Let it be V2.
Mv - mu = mV2 + M (V2 - u)
Mv - mu = mV2 + MV2 - Mu
Mv + Mu - mu = V2 *(M+m)
V2 = [Mv + Mu - mu]/(M+m)
iii] Vcart = V2 - u
= [Mv + Mu - mu]/(M+m) - u
= [Mv - 2mu]/(M+m)