A canoe has a velocity of 0.410m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.510m/s east relative to the earth. Find the magnitude of the velocity v⃗ c/r of the canoe relative to the river

draw the diagram.

.410SE=.510E+V

V= .410*.707S+.410*.707E-.510E

combine

just leave it

....such hard questions wont b asked...

To find the magnitude of the velocity v⃗ c/r of the canoe relative to the river, we can use vector addition.

First, let's break down the velocities into their horizontal and vertical components.

The velocity of the canoe relative to the earth has a magnitude of 0.410 m/s and is southeast. Since southeast is at a 45-degree angle between east and south, we can split this velocity into its horizontal and vertical components.

The horizontal component can be calculated using the cosine of the angle:

Horizontal component = magnitude * cos(angle)
= 0.410 m/s * cos(45°)
= 0.410 m/s * (√2 / 2)
= 0.2897 m/s (approx.)

The vertical component can be calculated using the sine of the angle:

Vertical component = magnitude * sin(angle)
= 0.410 m/s * sin(45°)
= 0.410 m/s * (√2 / 2)
= 0.2897 m/s (approx.)

Now, for the river velocity relative to the earth, we know that it has a magnitude of 0.510 m/s and is directed east. Since east is a horizontal direction, its vertical component is zero.

Therefore, the horizontal component of the canoe's velocity relative to the river is the difference between the horizontal components of the canoe and the river velocities:

Horizontal component = (0.2897 m/s - 0.510 m/s)
= -0.2203 m/s

The vertical component of the canoe's velocity relative to the river is the difference between the vertical components of the canoe and the river velocities:

Vertical component = (0.2897 m/s - 0)
= 0.2897 m/s

Now, we can use the Pythagorean theorem to find the magnitude of v⃗ c/r:

Magnitude of v⃗ c/r = √(horizontal component^2 + vertical component^2)
= √((-0.2203 m/s)^2 + (0.2897 m/s)^2)
≈ 0.367 m/s

Therefore, the magnitude of the velocity v⃗ c/r of the canoe relative to the river is approximately 0.367 m/s.