A boat moves north at a uniform velocity of 15 mph relative to the shore from one side of the river to a point directly opposite on the other side of the river. The water in the river flows east at a constant speed of 5mph parallel to the shore. What is the velocity of the boat relative to the water?

Can you elaborate more?? I don't understand it..

boatrelative/shore= waterrelativeshore+boarrelativewater

These are vectors
15N=5E+boatrelativewater

boatrelativewater= 15N-5E

Now we can use the right triangle.
first, the angle: The angle theta measured from directly across the river upstream, Theta= arcTan5/15

Now, the magnitude: v=sqrt(15^2+5^2)

Thank you....

To find the velocity of the boat relative to the water, we need to consider the velocity of the boat relative to the shore (given as 15 mph) and the velocity of the water in the river (given as 5 mph).

Since the boat is moving directly across the river, which is perpendicular to the shore, the velocity of the boat relative to the water will be the vector sum of its velocity relative to the shore and the velocity of the water in the river.

We can use vector addition to calculate this:

Let's say the velocity of the boat relative to the water is Vb/w (V for velocity, b for boat, and w for water).
Vb/w = Vb/s + Vw/s

Vb/s represents the velocity of the boat relative to the shore, and Vw/s represents the velocity of the water in the river relative to the shore.

Given:
Vb/s = 15 mph (velocity of the boat relative to the shore)
Vw/s = 5 mph (velocity of the water relative to the shore)

Substituting the given values:
Vb/w = 15 mph + 5 mph

Now, calculating:
Vb/w = 20 mph

Therefore, the velocity of the boat relative to the water is 20 mph.