What is the Velocity of the River's Current?

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SUMMARY

The velocity of the river's current can be determined using trigonometric relationships involving the boat's speed and the angle of travel. In this case, a boat with a speed of 1.70 m/s must head at a 45-degree angle to cross a 260-meter wide river and arrive 110 meters upstream. The correct calculation for the river's current speed (Vws) is derived from the equation sin(Theta) = Vws/Vbs, leading to a current speed of 1.20 m/s. However, this calculation fails to account for the downstream drift caused by the current, necessitating a reevaluation of the trajectory to ensure the boat lands at the desired point.

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  • Understanding of basic trigonometry, specifically sine functions.
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  • Familiarity with the concept of relative velocity in fluid dynamics.
  • Ability to visualize and analyze motion in two dimensions.
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  • Study the principles of relative velocity in fluid dynamics.
  • Learn how to apply trigonometric functions to solve vector problems.
  • Explore graphical methods for visualizing motion in two dimensions.
  • Investigate the effects of current on navigation and boat trajectory.
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Students in physics, particularly those studying mechanics and fluid dynamics, as well as anyone involved in navigation or maritime operations who needs to understand the impact of water currents on vessel movement.

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Homework Statement


A boat whose speed in still water is 1.70m/s must cross a 260 meter wide river and arrive at a point 110 metres upstream from where it starts. To do so, the pilot must head the boat at a 45 degrees upstream angle. What is the speed of the river's current.

Homework Equations


According to my lecture, I believe the equation should be sin Theta = Vws/Vbs
Vws being the water's current, and Vbs the boat's speed. However, I don't know where the river's width comes in.

The Attempt at a Solution


Sin 45 = Vws/1.70 m/s
Vws = Sin 45 x 1.70
Vws = 1.20 m/s.

Would this be correct?

THANKS!
 
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No ideas?...
 
I don't believe you are correct. You are not taking into account that you want to land 110 m upstream. Draw a picture. You'll see that at the angle of 45 degrees, the distance traveled along the river bank (in direction of current) is more than 110 m. This is necessary because the river will push the boat downstream. What you have calculated is the upstream component of the boat's velocity, not the velocity of the river current.
 

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