Vectors Question using Calculus -- Swimmer crossing a River

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SUMMARY

The discussion centers on a physics problem involving Bob, who swims across a 200 m wide river with a current flowing westward at 2.5 m/s. Bob's swimming speed in still water is 4 m/s. To reach a point directly opposite his starting position, Bob must swim at an angle upstream, resulting in a velocity vector that combines both his swimming speed and the river's current. The solution involves constructing a vector triangle to determine Bob's resultant speed and direction relative to the ground.

PREREQUISITES
  • Understanding of vector addition and relative velocity
  • Familiarity with Pythagorean theorem for right triangles
  • Basic knowledge of swimming physics and motion in fluids
  • Ability to draw and interpret vector diagrams
NEXT STEPS
  • Study vector addition in physics, focusing on relative velocity concepts
  • Learn how to construct and analyze vector triangles in motion problems
  • Explore the Edexcel M4 textbook for practice on similar relative velocity problems
  • Investigate the effects of currents on swimming techniques and strategies
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Students studying physics, particularly those focusing on mechanics and vector analysis, as well as educators looking for practical examples of relative motion in fluid dynamics.

  • #31
ttpp1124 said:
Relative meaning in the direction of.

I know this is an old thread, but this just bothered me. Relative to does not mean 'in the direction of', relative to implies a subtraction i.e. 'from the perspective of'. A part of a vector in a certain direction is something different, i.e. a vector component / vector projection.
 

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