# A boat is going across a river. The river flows from south to north. If the boat is moving through the water at 4.3 m/s, and the river is flowing at 1.3 m/s, what is the velocity of the boat as...

A boat is going across a river. The river flows from south to north. If the boat is moving through the water at 4.3 m/s, and the river is flowing at 1.3 m/s, what is the velocity of the boat as seen from the shore?

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### 1 Answer

The boat is moving across the river at 4.3 m/s and the river water is flowing from south to north at 1.3 m/s. As the direction in which the boat is moving is not given, it is assumed to be east to west.

The velocity of the boat with respect to a person standing on the shore is the sum of the two vectors. One from south to north with a magnitude of 1.3 and the other from east to west with a magnitude of 4.3.

The magnitude of the boat's velocity is `sqrt(1.3^2 + 4.3^2) ~~ 4.49` m/s. The angle at which the boat moves is `tan^-1(1.3/4.3) = 16.82` degrees in the direction west of north.

**The velocity of the boat as seen by someone on the shore is 4.49 m/s at an angle 16.82 west of north**.