Related Rates: Calculating the Separation Between Two Moving Objects

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Discussion Overview

The discussion revolves around a related rates problem involving a train and a motorboat moving at right angles to each other. Participants explore how to calculate the rate at which the two objects are separating after a specific time interval, focusing on the application of calculus concepts to the scenario.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the problem involving a train and a motorboat, specifying their speeds and the height of the bridge.
  • Several participants express uncertainty about how to start solving the problem and request guidance.
  • A suggestion is made to visualize the scenario, prompting discussion about the geometric relationship between the train and motorboat as they move apart.
  • Another participant shares their approach using the Pythagorean theorem and differentiation to find the rate of separation.
  • There is a calculation presented that results in a separation rate of 63.2 km/h, which is later corrected to 62.8 km/h.
  • Participants discuss the importance of unit conversion and the potential for rounding errors in their calculations.
  • One participant questions the relevance of the height of the bridge in the calculations, while another asserts that it does not affect the differentiation process since it remains constant.
  • There is a mention of a textbook source for the problem, indicating a shared context among participants.

Areas of Agreement / Disagreement

Participants generally agree on the method of using related rates to approach the problem, but there are differing opinions on the correctness of the calculated separation rate, as well as the relevance of the height of the bridge in the calculations. The discussion remains unresolved regarding the exact answer and the implications of the height.

Contextual Notes

Some participants express uncertainty about their calculations and the assumptions made, particularly regarding unit conversions and the treatment of constant quantities in related rates. There is also mention of potential rounding issues affecting the final answer.

Who May Find This Useful

Students studying calculus, particularly those focusing on related rates problems, as well as individuals interested in applying mathematical reasoning to real-world scenarios involving motion.

sabrina_m33
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A railroad bridge is 20m above, and at right angles to, a river. A person in a train traveling at 60 km/h passes over the centre of the bridge at the same instant that a person in a motorboat traveling at 20km/h passes under the centre of the bridge. How fast are the two people separating 10s later?
 
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Please someone show me how to answer this!
Thanks!
 
Did you draw a picture? How does it look like?

Show your work please!
 
Only problem is I don't really know how to start!:(
 
Picture an aerial view. At some instance, the motorboat and train are at the same point. As they move further from each other (at right angles), what does their relationship start to resemble?

A triangle, rectangle, circle?
 
ok this is what i tried...d^2= x^2 + y^2
took derivative
2d*dd/dt=2x*dx/dt + 2y*dy/dt
factored a 2 out and emilinated and isoltaed for dd/dt
dd/dt = (x*dx/dt + y*dy/dt)/d
 
subed in the values of the corresponding speeds 10s later
dd/dt=[(16.66)(166.6)+(5.55)(55.5)] /175.68
=17.5
and when i covert back to km/h i get 63.2 km/h
the answer is supose to be 63.2 km/h
 
opps the answer is supose to be 62.8 km/h
 
It asks you to evaluate it at 10s. You're rates have units km/h.

Convert hours to seconds.
 
  • #10
and I never rounded any if my numbers, stored them all in my calc.
 
  • #11
yes I did convert.. the 60 km/h goes to 166.66m/s and the 20km/h to 5.55m/s
 
  • #12
sabrina_m33 said:
yes I did convert.. the 60 km/h goes to 166.66m/s and the 20km/h to 5.55m/s
Sorry, didn't notice since you didn't write them in your problem.
 
  • #13
it's ok. I don't really see what I am doing wrong, I thought I was approaching the question right, but if my teacher says that is the answer then i guess not!
 
  • #14
I got the same answer. Perhaps your teacher rounded off, who knows? Wouldn't worry too much.
 
Last edited:
  • #15
yeah maybe.. only problem is this is an assignment that's due for marks!
Well thank you for your help!:D
 
  • #16
Anytime, gl! Make 100s :)
 
  • #17
does the height of 20m have anything to do with the calculations?
 
  • #18
I got the same answer. and ur question no the 20m has nothing to do with the process for solving the question because the height between the bridge and the river does not change right ? so u do not need to differentiate that

Remember Related rates is only concerned with QUANTITIES THAT CHANGE ! lol sorry... i had to emphasize a point. This is what i learned from my hard times doing related rates and and... does anyone get another answer ? i got the same thing I am using Advanced FUnctions and Introductory Calculus from Harcourt Mathematics 12 . Thats where u got this question from lol and no from ur teacher llllooool <_<
 

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