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Precalc

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A boat that travels at 16 knots in calm water is sailing across a current of 3 knots on a river 250 m wide. The boat makes an angle of 35 degrees with the current heading into the current.

Find the resultant velocity of the boat. How far upstream is the boat when it reaches the other shore?

Do I need to use parametric equations to solve this? If so, how do I find the time? Thanks in advance.

  • Precalc - ,

    Boat velocity component upstream = 16 cos 35 - 3
    = 13.1 - 3
    = 10.1 kn
    Boat velocity component across stream = 16 sin 35 = 9.18 kn
    resultant speed = sqrt(10.1^2+9.18^2) = 13.6 kn
    tangent of resultant angle to upstream = 9.18/10.1 = .909
    so angle to upstream = tan^-1 .909 = 42.3 deg
    Now you do not have to know time T because
    distance upstream = 10.1 T
    distance across = 9.18 T
    distance upstream/distance across =10.1/9.18 (The T cancels
    so
    10.1/9.18 = distance upstream/250 meters
    so
    distance upstream = 250 * 10.1/9.18 = 275 meters
    That avoids having to convert nautical miles to meters. I suppose in a sense my use of T implies parametric :)

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