© Copyright, Department of Physics, University of Illinois at Urbana-Champaign

Stream Crossing

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Alice swims across a stream of width d = 300 ft. The stream flows from west to east with current speed vC of 10 ft / minute. If there were no current, as in a pool or a lake, Alice would swim with speed vA of 20 ft / minute, in the direction indicated in the picture above, f = 20 degrees. Find the position xo along the x-axis where she will come out across the stream. Note that

  • f is the angle between the y-axis and the swimmer's velocity
  • east (downstream) is defined as positive x, west (upstream) is defined as negative x

    For example, the x-component of the velocity pointing east is positive, and the x-component of the velocity pointing west is negative.

    If you enter an expression, use degrees as arguments for sin and cos, rather than radians.

    xo = ft