Final answer:
To calculate the velocity of the canoe relative to the river, one should break down the canoe's velocity into east and south components, subtract the east component from the river's eastward velocity, and then use the Pythagorean theorem for the resultant magnitude. Exact computation isn't possible without the angle of southeast direction.
Step-by-step explanation:
To find the magnitude of the velocity of the canoe relative to the river, we must consider the given velocities as vectors. The canoe's velocity southeast is given as 0.30 m/s, and the river's flow to the east is 0.53 m/s. Since southeast is a combination of south and east directions, the canoe's southeast velocity vector can be broken down into two components: one south and one east.
However, to find the magnitude of the canoe's velocity relative to the river, we only need to consider the components of velocity perpendicular to the river's flow, because velocities in the same direction (east, in this case) will add up or subtract directly. In our case, since the river flows due east, the canoe's velocity component going directly east will be subtracted from the river's eastward velocity to determine the canoe's effective velocity relative to the river's flow.
For example, if a canoe is heading east at 0.30 m/s, and the river flows east at 0.53 m/s, then relative to the river, the canoe is actually moving west (against the flow) with a velocity of 0.53 m/s - 0.30 m/s = 0.23 m/s.
To solve the provided problem precisely, we would decompose the canoe's southeast velocity into east and south components, subtract the east component from the river's flow, and then use the Pythagorean theorem to find the resultant magnitude. Unfortunately, we do not have sufficient information to calculate the exact values, as the angle of southeast is not provided.