Swimming Speed in a River: Calculating Resultant Velocity

To determine how fast you are going, you can use the concept of vector addition. Since you are swimming north at 1 m/s and the river's water is flowing east at 0.3 m/s, the two velocities can be treated as vectors.

To find the resultant velocity, you can use the Pythagorean theorem. The northward velocity is 1 m/s, and the eastward velocity is 0.3 m/s. Thus, you can form a right triangle:

The magnitude of the resultant velocity (V) is given by: V = √((1 m/s)^2 + (0.3 m/s)^2)

V = √(1 + 0.09) = √1.09 ≈ 1.043 m/s

Therefore, you are traveling at approximately 1.043 m/s in the direction formed by the resultant vector, which is slightly north-east.