find the distance that the crate slides relative to the platform: Do not round i

Question

find the distance that the crate slides relative to the platform:

Do not round intermediate calculations, however for display purposes report intermediate steps rounded to four significant figures. Give your final answer(s) to three significant figures. A 727 lb floating platform is at rest when a 197 lb crate is thrown onto it with a horizontal speed v_0 = 13 ft/s. Once the crate stops sliding relative to the platform, the platform and the crate move with a speed v = 2.697 ft/s. Neglecting the vertical motion of the system as well as any resistance due to the relative motion of the platform with respect to the water, determine the distance that the crate slides relative to the platform if the coefficient of kinetic friction between the platform and the crate is mu k = 0.22.

Explanation / Answer

here

using work energy principle,

KE i + PE i   = KEf + PEf

0.5 mvi^2 + 0   = 0.5 mVf^2 + mgh

g = 32 ft/s^2

0.5*197*13^2 = 0.5*727*2.697^2 + 0.22*197*32 * s

s = 10.1 ft (ANSWER)

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