A canoe has velocity of 0.40m/s southwest relative to earth.the canoe is on a river that is flowing 0.50m/s east relative to earth find the velocity (magnitude and direction) of the canoe relative to the river.

4OM/M VELOCITY EQUAL MAGNITUDE AND DIRECTION

To find the velocity of the canoe relative to the river, you need to use vector addition. The velocity of the canoe relative to the river can be calculated by subtracting the velocity of the river from the velocity of the canoe.

Let's break the velocities down into their components.

The velocity of the canoe relative to the Earth is given as 0.40 m/s southwest. This means that the canoe is moving in the direction 225 degrees (southwest) with a speed of 0.40 m/s.

The velocity of the river relative to the Earth is given as 0.50 m/s east. This means that the river is flowing in the direction 90 degrees (east) with a speed of 0.50 m/s.

To find the velocity of the canoe relative to the river, we subtract the velocity of the river from the velocity of the canoe.

To do this, we break down the velocities into their x and y components. The x-direction is east and the y-direction is north.

The velocity of the canoe relative to the Earth can be represented as follows:
Vcanoex = 0.40 m/s * cos(225 degrees) (x-component)
Vcanoey = 0.40 m/s * sin(225 degrees) (y-component)

The velocity of the river relative to the Earth can be represented as follows:
Vriverx = 0.50 m/s * cos(90 degrees) (x-component)
Vrivery = 0.50 m/s * sin(90 degrees) (y-component)

Now, we subtract the x-components and y-components of the river from the canoe:
Vcanoex - Vriverx = Vcanoerelativex
Vcanoey - Vrivery = Vcanoerelativey

Finally, we can use the Pythagorean theorem to find the magnitude of the velocity and the inverse tangent function to find the direction.

Magnitude = sqrt(Vcanoerelativex² + Vcanoerelativey²)
Direction = tan^(-1)(Vcanoerelativey / Vcanoerelativex)

Plugging in the values, you can calculate the magnitude and direction of the velocity of the canoe relative to the river.

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