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Powerboat moving at an angle across a river with current

  1. Sep 11, 2009 #1
    1. The problem statement, all variables and given/known data
    A 210-m-wide river has a uniform flow speed of 2.4 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 8.4 m/s with respect to the water. There is a clearing on the north bank 17 m upstream from a point directly opposite the clearing on the south bank. (a) At what angle, measured relative to the direction of flow of the river, must the boat be pointed in order to travel in a straight line and land in the clearing on the north bank? (b) How long will the boat take to cross the river and land in the clearing?

    2. Relevant equations
    Superimpose an xy coordinate system, with the water moving in the positive x direction. The time required to cross the river width is the same as the time to move upstream to the clearing. Thus the boat's velocity bg relative to the shore must have a negative x component.

    3. The attempt at a solution
    Find the x and y components of the vector. Use arctan to find the angle. arctan(210/17) =85.37186
    2.4t - 8.4cos (theta)t = 17
    8.4sin(theta)t = 210
    solve for t to find theta.
    I've tried a ton of methods but I'm not getting the right answer. Please help.
    Last edited: Sep 11, 2009
  2. jcsd
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