Calculating Velocity in Two Dimensions: A Real-Life Swimming Challenge

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SUMMARY

The swimmer's velocity with respect to the crowd observing from the beach is calculated to be 3.63 m/s at a direction of N 30 degrees E. The swimmer maintained a northward velocity of 4 m/s while encountering a cross-current of 2 m/s directed E 25 degrees S. The calculations involved breaking down the velocities into components using trigonometric functions and applying the Pythagorean theorem to find the resultant velocity. The final direction was determined using the tangent function.

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  • Understanding of vector addition in physics
  • Knowledge of trigonometric functions (sine, cosine, tangent)
  • Familiarity with the Pythagorean theorem
  • Basic concepts of velocity and direction in two dimensions
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  • Learn advanced applications of trigonometry in physics problems
  • Explore real-life applications of velocity calculations in swimming and other sports
  • Investigate the effects of currents on swimming trajectories
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This discussion is beneficial for physics students, swimming coaches, and anyone interested in understanding the impact of currents on swimming performance and velocity calculations in two dimensions.

Mary1910
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Question:
In an anniversary celebration of Marilyn Bell's 1954 feat- she was the first person to swim across Lake Ontario- a swimmer set out from the shores of New York and maintained a velocity of 4m/s (N). As the swimmer approached the Ontario shore, she encountered a cross-current of 2 m/s (E 25 degrees S) - 25 degrees South of East. Calculate her velocity with respect to the crowd observing from the beach (with respect to the ground).

My Attempt at a Solution:

First I drew a triangle. 4m/s (N) is the left side of the triangle. 2m/s (E 25 degrees S) is the top of the triangle. And the right side is the side that I think that I am solving for.

Next I divided the triangle into two right angled triangles.

Solving for the top triangle:

sin=Opposite/Hypotenuse
=2sin(65)
=1.81 m/s

cos=Adjacent/Hypotenuse
=2cos(65)
=0.845 m/s
=0.85m/s

To solve for the bottom triangle:

4m/s - 0.85m/s = 3.15m/s

Use Pythagorean theorem to solve for the unknown side:

3.15^2 + 1.81^2
=3.63m/s

Calculate the direction of the velocity:

tan=ay/ax
tan=1.81/3.15
=29.88
=30 degrees

Therefore her velocity, with respect to the crowd observing from the beach is 3.63m/s (N 30 degrees E)

Could someone please let me know if my calculations are correct? I would appreciate the help. :)
 
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