Final answer:
The speed of the boat in still water can be found by considering the velocity of the boat with respect to the Earth. By using vector addition and the Pythagorean theorem, we can calculate the magnitude of the velocity to be approximately 5.41 m/s.
Step-by-step explanation:
The speed of the boat in still water can be found by considering the velocity of the boat with respect to the Earth. In this case, we can use the given information:
The boat heads north in still water at a speed of 4.5 m/s.
The river is running east at a speed of 3.0 m/s.
To find the velocity of the boat with respect to Earth, we can use vector addition. Since the boat is heading north and the river is running east, we can treat this as a right triangle. Using the Pythagorean theorem, we can find the magnitude of the velocity:
Velocity = sqrt((4.5 m/s)^2 + (3.0 m/s)^2) = sqrt(20.25 m^2/s^2 + 9 m^2/s^2) = sqrt(29.25 m^2/s^2) ≈ 5.41 m/s
Therefore, the speed of the boat in still water is approximately 5.41 m/s.