How to Calculate the Correct Angle and Time to Cross a River in a Powerboat?

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SUMMARY

The discussion centers on calculating the correct angle and time for a powerboat to cross a 310-meter-wide river with a flow speed of 1.6 m/s. The powerboat has a speed of 4.4 m/s relative to the water. To reach a clearing on the north bank that is 11 meters upstream, the boat must be pointed at a specific angle relative to the river's flow. The calculations reveal the necessary angle and the time required to cross the river, ensuring the boat lands accurately in the designated clearing.

PREREQUISITES
  • Understanding of vector components in physics
  • Knowledge of relative velocity concepts
  • Familiarity with trigonometric functions for angle calculations
  • Basic principles of motion in fluid dynamics
NEXT STEPS
  • Calculate the angle using trigonometric functions for vector resolution
  • Determine the time taken to cross the river using the formula for distance and speed
  • Explore the effects of varying river flow speeds on crossing angles
  • Investigate real-world applications of these calculations in navigation and boating
USEFUL FOR

Marine engineers, physics students, navigators, and anyone involved in powerboat operation or river crossing strategies will benefit from this discussion.

chaudown
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A 310-m-wide river has a uniform flow speed of 1.6 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 4.4 m/s with respect to the water. There is a clearing on the north bank 11 m upstream from a point directly opposite the clearing on the south bank. (a) At what angle, measured relative to the direction of flow of the river, must the boat be pointed in order to travel in a straight line and land in the clearing on the north bank? (b) How long will the boat take to cross the river and land in the clearing?


I don't know whether the 4.4 m/s is a magnitude or the y-component.
 
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chaudown said:
An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 4.4 m/s with respect to the water.

I don't know whether the 4.4 m/s is a magnitude or the y-component.
What is speed in relation to velocity?
 
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