River and boat velocity problem

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SUMMARY

The river and boat velocity problem involves a river flowing east at 1.20 m/s and a boat crossing from south to north at a velocity of 9.0 m/s relative to the water. The resultant velocity of the boat relative to the shore is calculated to be 9.08 m/s at an angle of 82.406 degrees north of east. To determine how far downstream the boat has moved while crossing a 380m wide river, one must first calculate the time taken to cross the river using the formula time = distance/velocity, which results in approximately 42 seconds. Multiplying this time by the river's current velocity yields the downstream displacement.

PREREQUISITES
  • Understanding of vector components and resultant velocity
  • Familiarity with the Pythagorean theorem
  • Knowledge of basic kinematics equations
  • Ability to perform trigonometric calculations
NEXT STEPS
  • Calculate the time taken for the boat to cross the river using the formula time = distance/velocity
  • Determine the downstream distance using the formula downstream distance = river current velocity × time
  • Explore vector addition in physics for more complex motion problems
  • Review kinematic equations for projectile motion to understand similar scenarios
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and vector analysis, as well as educators seeking to explain real-world applications of these concepts.

akbro93704
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Homework Statement



(1) A River flows due east at 1.20 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 9.0 m/s due north relative to the water. I got the velocity of the boat relative to shore at 9.08 m/s at 82.406 degrees north of east. What about if the river is 380m wide, how far downstream has the boat moved by the time it reaches the north shore?

Homework Equations





The Attempt at a Solution


I got the velocity by setting up components and using the Pythagorean theorem and tangent. What do I do with the 380m to figure out how far downstream the boat has moved by the time it reaches north shore? thanks
 
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How long does it take for the boat to cross the river?
 

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