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Math Help - How far in first minute?

  1. #1
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    Question How far in first minute?

    hey guys, i think i might have to use dv/dt = -kv. i have no idea how do this problem, help me solve this

    Suppose that a motorboat is moving at 40 ft/s when its motor suddenly quits, and that 10sec later the boat has slowed down to 20 ft/s. Assume that the resistance it encouters while coasting is proportional to the squire of its velocity. how far does the motorboat coast in the first minute after its motor quits?
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  2. #2
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    Quote Originally Posted by DMDil View Post
    hey guys, i think i might have to use dv/dt = -kv. i have no idea how do this problem, help me solve this

    Suppose that a motorboat is moving at 40 ft/s when its motor suddenly quits, and that 10sec later the boat has slowed down to 20 ft/s. Assume that the resistance it encouters while coasting is proportional to the squire of its velocity. how far does the motorboat coast in the first minute after its motor quits?
    I assume that's "square" ...

    \frac{dv}{dt} = -kv^2

    \frac{dv}{v^2} = -k \, dt

    -\frac{1}{v} = -kt + C

    v = \frac{1}{kt+C}

    use your given speeds and times to find k and C
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