Estimating Average Ocean Current Speed Using Trapezoidal Rule

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Homework Help Overview

The discussion revolves around estimating the average speed of ocean currents using the trapezoidal rule, based on given speed data at specific times. The subject area includes numerical integration and applications of calculus in real-world scenarios.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply the trapezoidal rule to estimate average speed but encounters an unexpectedly large result. Participants inquire about the methods used, including whether a speed-time graph was drawn and how the area under the curve was calculated.

Discussion Status

Some participants are actively questioning the original poster's approach and calculations, seeking clarification on the steps taken. There is an indication of exploration into the method, but no consensus or resolution has been reached as the original poster later states they figured it out.

Contextual Notes

There is a mention of converting time into hours and the use of specific data points for the trapezoidal rule, but the original poster's calculations led to confusion regarding the resulting average speed.

chukie
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Ocean currents (miles/hr) at a certain location are given below

Time of day: Speed mph:
8:00 am 17
8:10 am 20
8:20 am 22
8:30 am 21
8:40 am 17

How can I estimate the average river current speed from 8:00 am to 8:40 am using the trapezoidal rule? I tried but I got a huge number.
 
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What exactly did you do? Did you draw out the speed-time graph of these points and then attempt to find the area underneath after connecting all the dots?
 
Defennder said:
What exactly did you do? Did you draw out the speed-time graph of these points and then attempt to find the area underneath after connecting all the dots?

I converted 8:40 into hours so 40/60=2/3
Then I supposed 0 to be 8:00, so the equation I had was integral sign 0 to 2/3 S(t) dt.
Then using the data in the chart: (17+2(20)+2(22)+2(21)+17)
Then I multiplied that sum by 1/(b-a) to get the average, and I got a number in the hundreds.
 
Last edited:
nvm i got it
 

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