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.
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
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