A canoe has a velocity of 0.39 southeast relative to the earth. The canoe is on a river that is flowing 0.59 east relative to the earth.
Find the magnitude of the velocity of the canoe relative to the river.
Find the direction of the velocity of the canoe relative to the river
Do a vector subtraction of the river water velocity from the velocity of the canoe relative to earth.
Velocity relative to Earth
= 0.27577 i - 0.2577 j
(i is east unit vector; j is north unit vector)
Velocity of river relative to Earth
= 0.59 i
Velocity of canoe relative to water:
= -0.31423 i -0.2577 j
magnitude of above = 0.4064
You forgot to include the dimension of the velocity number.
To find the magnitude of the velocity of the canoe relative to the river, we can use vector addition.
The canoe's velocity relative to the earth is given as 0.39 southeast. Let's break this down into its horizontal and vertical components.
The southeast direction can be split into two components: east and south. Since the canoe's velocity is southeast, we can say that the horizontal component is in the east direction and the vertical component is in the south direction.
Given that the river is flowing 0.59 east relative to the earth, we can add this vector to the canoe's velocity relative to the earth to find the canoe's velocity relative to the river.
To find the magnitude of the velocity of the canoe relative to the river, we need to find the resultant vector by adding the horizontal and vertical components.
The horizontal component is 0.39 in the east direction, and the vertical component is 0 in the north-south direction. So the resultant vector is simply 0.39 in the east direction.
Therefore, the magnitude of the velocity of the canoe relative to the river is 0.39 units.
To find the direction of the velocity of the canoe relative to the river, we use the direction of the resultant vector, which is in the east direction. So the direction of the velocity of the canoe relative to the river is east.