Alice swims across a stream of width d=300 ft. The stream flows from West to Eas

Question

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 xo along the x-axis where will she come out across the stream.
(Note: upstream f is negative, downstream f is positive, f=0 for the velocity of the swimmer along the y-axis.)

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

Explanation / Answer

Width of stream=91.44m

speed of current=3.048/60 m/s=0.0508 m/s

alice's speed=0.1016 m/s

The vertical component of her speed=0.1016*cos(20)=0.09547 m/s

time taken to cross the stream=91.44/0.09547=957.76 s

The horizontal velocity of alice wrt the ground=0.0508-0.1016 Sin20=0.01605 m/s

The horizontal distance covered=0.01605*957.76= 15.4m=50.4 ft

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