Ethan, whose mass is M E = 87 kg , stands at one end of a very long, stationary

Question

Ethan, whose mass is ME= 87 kg , stands at one end of a very long, stationary wheeled cart that has a mass of Mc= 850 kg . He then starts sprinting toward the other end of the cart. He soon reaches his top speed of vE=8.0 m/s, measured relative to the cart.

Part A:

Write an expression for the velocity of the cart vC,f when Ethan has reached his top speed.

Assume that Ethan is moving in the positive-x direction. Give your answer in terms of some or all of the listed variables (ME, MC, vE) and any necessary constants. Use the appropriate sign to indicate the cart's direction.

Part B:

What is the speed of the cart with respect to the ground when Ethan has reached his top speed?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

In the initial frame of reference,
Ve = 8 - Vc and
Me*Ve = Mc*Vc (Conservation of momentum)
These 2 combine to give
Vc = 8*Me/[Mc*(1+Me/Mc)] = 8*87/[850*(1+87/850)] = 0.743 m/s

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