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

In summary, by using the Pythagorean theorem and trigonometric functions, the velocity of the swimmer with respect to the crowd observing from the beach was calculated to be 3.63m/s (N 30 degrees E).
  • #1
Mary1910
31
1
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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  • #2
Looks right to me.
 
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Likes Mary1910

1. What is the difference between scalar and vector quantities in motion?

Scalar quantities only have magnitude, such as speed or distance, whereas vector quantities have both magnitude and direction, such as velocity or displacement. In motion, scalar quantities can be represented by a single number while vector quantities require both a magnitude and direction to be fully described.

2. How is velocity calculated in two dimensions?

In two dimensions, velocity is calculated by dividing the total displacement in both the x and y directions by the total time taken. This gives the average velocity in two dimensions. To find the instantaneous velocity at a specific point, the slope of the tangent to the displacement-time graph at that point can be calculated.

3. What is the difference between distance and displacement in two dimensions?

Distance is the total length covered by an object, regardless of direction, while displacement is the shortest distance between the starting point and ending point of an object's motion. Displacement also includes the direction of motion, making it a vector quantity.

4. How do you calculate acceleration in two dimensions?

Acceleration in two dimensions is calculated by dividing the change in velocity in both the x and y directions by the total time taken. This gives the average acceleration in two dimensions. To find the instantaneous acceleration at a specific point, the slope of the tangent to the velocity-time graph at that point can be calculated.

5. How do you deal with projectile motion in two dimensions?

Projectile motion refers to the motion of an object that is only affected by gravity. To calculate the motion of a projectile in two dimensions, the horizontal and vertical components of the motion must be treated separately. The horizontal component of motion is constant, while the vertical component is subject to acceleration due to gravity. By using equations of motion and trigonometry, the trajectory of a projectile can be determined in two dimensions.

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