A canoe has a velocity of 0.50 m/s southeast relative to the earth. The canoe is on a river that is flowing 0.55 m/s east relative to the earth.
To find the actual velocity of the canoe, we need to find the vector sum of its velocity relative to the earth and the velocity of the river relative to the earth.
Given Information:
Velocity of the canoe relative to the earth = 0.50 m/s southeast
Velocity of the river relative to the earth = 0.55 m/s east
We can break down the velocity of the canoe into its components along the east and north directions. The southeast direction can be considered as a combination of east and south directions.
Let's assume that the velocity of the canoe along the east direction is Ve and the velocity along the north direction is Vn.
Now, we can break down the velocity of the canoe and the river into their east and north components:
Velocity of the canoe:
Ve(canoe) = 0.50 m/s * cos(45°) (since southeast is at a 45° angle to the east direction)
Vn(canoe) = -0.50 m/s * sin(45°) (since south is opposite to the north direction)
Velocity of the river:
Ve(river) = 0.55 m/s (as the river is flowing east, there is no northward component)
Vn(river) = 0 (as the river is flowing east, there is no northward component)
Now, we can find the actual velocity of the canoe by adding the velocity of the canoe and the velocity of the river in each direction:
Actual velocity of the canoe (Ve,actual) = Ve(canoe) + Ve(river)
Actual velocity of the canoe (Vn,actual) = Vn(canoe) + Vn(river)
Substituting the values we found earlier:
Ve,actual = 0.50 m/s * cos(45°) + 0.55 m/s
Vn,actual = -0.50 m/s * sin(45°) + 0
Now, you can calculate the values by plugging them into a calculator:
Ve,actual = 0.50 m/s * cos(45°) + 0.55 m/s
Ve,actual = 0.35 m/s + 0.55 m/s
Ve,actual = 0.90 m/s (rounded to two decimal places)
Vn,actual = -0.50 m/s * sin(45°) + 0
Vn,actual = -0.35 m/s + 0
Vn,actual = -0.35 m/s
Therefore, the actual velocity of the canoe is approximately 0.90 m/s east and -0.35 m/s north relative to the earth.