Velocity in a Moving Frame| University Physics

You are attempting to row across a stream in your rowboat. Your paddling speed relative to still water is 3.0 m/s (i.e., if you were to paddle in water without a current, you would move with a speed of 3.0 m/s ). You head off by rowing directly north, across the stream. Assume that the stream flows east at 4.0 m/s, determine how far downstream of your starting point you will finally reach the opposite shore if the stream is 6.0 meters wide.

The figure shows a top view of a rowboat moving in the north direction across a stream. The north direction coincides with the top direction on this figure, and the east direction coincides with the direction to the right on this figure.

ANSWER: 8.0\:m

The total velocity of your motion is the vector sum of the velocity you would have in still water and the velocity of the stream. To add two vectors, place the tail of the second vector at the tip of the first. Together, the two vectors now form two legs of a triangle. The sum of these two vectors is the third side of this triangle. The tail of the sum should coincide with the tail of the first vector, and the tip of the sum should coincide with the tip of the second vector. Place the vectors carefully to be sure that your sum vector is accurate.

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Notice that your velocity has been given in component form: 3.0 m/s across the stream and 4.0 m/s along the stream. Based on these velocity components, it would take you 2.0 seconds to cross the 6.0 meter wide stream.

In two seconds, you would have traveled 

d=v_xt=\left(4.0\:m/s\right)\left(2\:s\right)=8.0\:m

downstream.

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