Physics Boat Problem involving velocity

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SUMMARY

The Physics Boat Problem involves calculating the velocity of a boat crossing a river with a current. The river is 209 meters wide, flowing east at 2.2 m/s, while the boat has a speed of 8.3 m/s relative to the water, directed 30° west of north. The correct magnitude of the boat's velocity relative to the ground is determined by vector addition, accounting for both the boat's speed and the river's current. Understanding the concept of "relative to the water" is crucial for solving this problem accurately.

PREREQUISITES
  • Vector addition in physics
  • Understanding of relative velocity
  • Basic trigonometry for angle calculations
  • Knowledge of motion in two dimensions
NEXT STEPS
  • Study vector addition techniques in physics
  • Learn about relative velocity concepts
  • Practice problems involving motion in two dimensions
  • Explore trigonometric functions for angle resolution
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Students studying physics, particularly those focusing on mechanics and motion, as well as educators looking for examples of relative velocity problems.

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Homework Statement


1. A river that is 209 m wide flows due east at a uniform speed of 2.2 m/s. A boat with a speed of 8.3 m/s relative to the water leaves the south bank pointed in a direction 30° west of north.
(a) What is the magnitude of the boat's velocity? (m/s)
(b) What is the direction of the boat's velocity relative to the ground? (answer in degrees west of north)
(c) How long does the boat take to cross the river? (s)



The Attempt at a Solution


For part a, I tried a few answers such as 16.6, 7.188, 7.2, 4.15, 7.19, but none of those answers were right. I think my main problem is understanding the question, perhaps i misunderstood the "relative to the water" part. Can someone please explain it to me. The right answer would also be appreciated.
 
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"relative to the water" means in the reference frame of the water. note the water is moving "relative to the ground" (or as seen in the frame of the ground). but if you are IN the ref frame of water, then the "ground is moving" instead. as a result, the velocity relative to water would be different from the velocity relative to the ground, for example.
 

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