Problem 9 The mercury skaters of Adebaran 7 don\'t really skate; it\'s closer to

Question

Problem 9 The mercury skaters of Adebaran 7 don't really skate; it's closer to water skiing. They attach themselves to floating rocket engines, strap on their skis and shoot across the vast open pools of mercury that cover the surface of the planet. Barklod is a mercury skating enthusiast, but she can only afford a pretty cheap engine that only provides a thrust of 60 . Her skis aren't the high quality frictionless ones, either and the mercury pools provide a resistance proportional to the cube of her velocity Last time she measured her equipment, she found that when she's travelling at 3", her acceleration is already down to 6 What is the fastest she can go with her equipment?

Explanation / Answer

anet = athrust - resistance

anet = athrust - bv3 (where b is constant of proportionality)

=> anet = 60 - bv3

Now given anet = 6 when v = 3

Therefore , 6 = 60 - b(3)3 => 27b = 60 - 6 = 54 => b = 54/27 = 2

Hence , anet = 60 - 2v3

v max => dv/dt = 0 => anet = 0 => 60 - 2vmax3 = 0 => vmax3 = 30 => vmax = (30)1/3 = 3.10 m/s

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