Approximating Position with Riemann Sums

In summary, a Ferris wheel is an amusement ride with rotating compartments attached to a wheel. It was invented by George Washington Gale Ferris Jr. for the 1893 World's Columbian Exposition. A Riemann Sum is a calculus method used to approximate the area under a curve, and it can be applied to the motion of a Ferris wheel by calculating the area under its rotation. Both the Ferris wheel and Riemann Sum have practical applications in real-world situations such as modeling pendulum motion and predicting market prices. They are also commonly used in engineering and physics.
  • #1
astasiamancini
1
0
The question provides a table of values for time and velocity.

Part c of the question asks to use a Riemann sum to approximate (not specifying which one). Part d asks what the answer to part c represents and to explain my reasoning. The answer that I got for the sum is 58.5 feet, but I do not know what this really means.
 
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  • #2
As velocity is the time rate of change of position, then such a summation of velocities will approximate the change in position. It would be helpful though if you posted the problem in its entirety. :D
 

1. What is a Ferris Wheel?

A Ferris wheel is a type of amusement ride consisting of a rotating upright wheel with multiple passenger compartments attached to the rim. It is commonly found in theme parks and carnivals.

2. Who invented the Ferris Wheel?

The Ferris wheel was invented by George Washington Gale Ferris Jr. for the 1893 World's Columbian Exposition in Chicago.

3. What is a Riemann Sum?

A Riemann Sum is a method used in calculus to approximate the area under a curve by dividing it into smaller rectangles and finding the sum of their areas.

4. How is the Riemann Sum used in relation to a Ferris Wheel?

The Riemann Sum can be used to calculate the area under the curve of the Ferris wheel's motion. By dividing the wheel's rotation into smaller time intervals, the height of the wheel at each interval can be used to calculate the area under the curve, which represents the distance traveled by the wheel.

5. Can the Ferris Wheel and Riemann Sum be applied in real-world situations?

Yes, the Ferris Wheel and Riemann Sum can be used to model and analyze various real-world situations, such as the motion of a pendulum or the changing market prices of goods. They are also commonly used in engineering and physics to make predictions and solve problems.

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