Final answer:
The canoe's actual speed in the river is found by using the Pythagorean theorem to combine the northward velocity of the canoe with the eastward velocity of the river current, resulting in a resultant speed of approximately 10.2 m/s.
Step-by-step explanation:
To find the canoe's actual speed in the river, we need to consider the velocity at which the canoe is trying to cross the river (towards the north) and the velocity of the river current (flowing east). These velocities need to be combined vectorially to find the resultant velocity, which will give us the actual speed of the canoe relative to the riverbanks.
The velocity of the canoe is 10 m/s north, and the river current is 2.0 m/s east. Since these two velocities are perpendicular to each other, we can use the Pythagorean theorem to find the resultant velocity:
Resultant velocity = \(√{(10 m/s)^2 + (2 m/s)^2}\) = \(√{100 + 4}\) = \(√{104}\) m/s
After calculating, we find that the resultant velocity is approximately 10.2 m/s. Therefore, the canoe's actual speed in the river is 10.2 m/s.
We do not consider any forces in this scenario because we are only asked to find the resultant velocity, not force.