calculus

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A boat is pulled into a dock by a string attached to the bow of the boat and passing through a pulley on the dock that is1ft higher than the bow of the boat. If the string is pulled at a rate of 3 ft/second, how fast is the boat approaching the dock when it is 7 ft from the dock?

  • calculus -

    Make a diagram, you should have a right-angled triangle.
    let the horizontal distance of the boat from the dock be x ft
    let the hypotenuse, the length of the rope, be y ft.

    then x^2 + 1^2 = y^2
    2xdx/dt = 2ydy/dt

    when x=7
    y^2 = 7^2 + 1^ = 50
    y = √50
    and you are given dy/dt = -3 ft/s (I made it negative since y is decreasing)

    sub in and you are on your way.

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