How to Calculate Time and Displacement for a Ferry Boat Crossing a River?

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SUMMARY

The discussion focuses on calculating the time and displacement for a ferry boat crossing a river with a width of 850 meters. The average velocity of the water relative to the shore is 3.8 m/s east, while the ferry boat's velocity relative to the water is 4.9 m/s south. The calculated velocity of the ferry boat relative to the shore is 6.2 m/s at an angle of 52 degrees south of east. The main challenges discussed include determining the crossing time and the displacement of the boat during the crossing.

PREREQUISITES
  • Understanding of vector addition in physics
  • Knowledge of relative velocity concepts
  • Familiarity with basic kinematic equations
  • Ability to perform trigonometric calculations for angle determination
NEXT STEPS
  • Calculate the time taken for the ferry boat to cross the river using the formula: time = distance / velocity.
  • Determine the displacement of the ferry boat using vector components and trigonometric functions.
  • Explore the concept of relative velocity in more depth, particularly in multi-vector scenarios.
  • Review kinematic equations related to motion in two dimensions for further applications.
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This discussion is beneficial for physics students, educators, and anyone interested in understanding vector motion and relative velocity in real-world scenarios, particularly in navigation and transportation contexts.

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Homework Statement



A ferry boat is crossing a river that is 8.5 x 10^2m wide. The average velocity of the waer relative to the shore is 3.8m/s (e) and the average velocity of the boat relative to the water is 4.9m/s (s).

Homework Equations





The Attempt at a Solution


So i got the first part down where it says to determine velocity of the ferry boat relative to the shore. I got 6.2m/s [E52*S].

part b) and c) is what i don't get.

b) How long does the crossing take?

c) Determine the displacement of the boat as it crosses from the north shore to the south shore.

Also another thing that confuses me is the velocities. Should it be for example water to shore, shore to boat, boat to water? Instead its like water to shore, boat to water, then it asks boat to shore. I don't know if its big deal but was just wondering because in examples in our book it has it going in order if that makes sense.
 
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You have three vectors, given any two you can calculate third - so order doesn't matter.

You are given distance, you are given velocity, where is the problem with calculating time? I guess velocity of the boat relative to water is perpendicular to shore, which makes calculations pretty simple.
 

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