Question

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.
Now assume that the stream flows east at 4.0 m/s. Draw the vectors $\vec{v}_w$, representing the velocity of the stream, and $\vec{v}_{tot}$, representing the velocity of your rowboat relative to the stream bank. Be sure to draw both vectors.
Draw $\vec{v}_{tot}$ and $\vec{v}_w$ starting at the tail and tip of $\vec{v}_{still}$ respectively. The location, orientation and length of the vectors should be appropriate. Each vector's length is displayed in meters per second.

Answer 1

Answer:

Please check the attached file for the diagram

Explanation:

The velocity of the of the rowboat $V_{tot}$  through the river is the resultant velocity. It is obtained taking a vector sum of the velocity in still water and the velocity of the river.

There are several ways to take this vector sum, but the question makes it simple for us to use Pythagoras's theorem because the East and North directions are perpendicular to each other.

Hence;

$V_{tot}^2=V_{still}^2+V_{w}^2\\V_{tot}^2=3^2+4^2$

$V_{tot}=\sqrt{3^2+4^2}\\ V_{tot}=\sqrt{25}=5m/s$