Final answer:
The magnitude of the canoe's velocity relative to the river, calculated using the Pythagorean theorem, is 15.8 m/s. The direction of this resultant velocity will be at an angle of roughly 18.4 degrees to the right of the straight-line path intended by the rower.
Step-by-step explanation:
To find the magnitude of the velocity of the canoe relative to the river, we need to consider both the velocity of the canoe and the velocity of the river. Given that the canoe attempts to travel at a speed of 15 m/s relative to the still water, and that the river flows at 5.0 m/s, we need to calculate the resultant velocity vector using vector addition.
We can find the resultant velocity using the Pythagorean theorem because the velocity of the canoe is perpendicular to the flow of the river. The formula for the magnitude of the resultant velocity (Vcr) is: Vcr = √(Vcanoe² + Vriver²).
Plugging in the values we get: Vcr = √(15² + 5²) = √(225 + 25) = √(250).
Therefore, Vcr = 15.8 m/s. This is the resultant velocity of the canoe relative to the river. Direction relative to the straight line can be found using the arctan function to find the angle, which would be arctan(5/15), giving an angle of approximately 18.4 degrees to the right of the intended straight path across the river.