A river that is flowing due west is crossed by a boat travelling from the south bank to the north bank. The boat can travel at 30 m/s in still water and the river is moving at 10 m/s.
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Determine the direction the boat must point to travel directly across. Express the direction using either the Navigator Method or the Polar Coordinates Method
To determine the direction the boat must point to travel directly across the river, we can use the Navigator Method.
1. Calculate the angle at which the boat must point:
tan(theta) = velocity of the river/velocity of the boat
tan(theta) = 10 m/s / 30 m/s
theta = arctan(1/3)
theta ≈ 18.43 degrees
2. Since the river is flowing due west, we need to add 90 degrees to the calculated angle to account for the direction of the river:
18.43 degrees + 90 degrees = 108.43 degrees
Therefore, the boat must point in a direction of approximately 108.43 degrees (measured clockwise from north) to travel directly across the river.