Rates of Change Question

sabrina_m33 · Mar 14, 2008

A railroad bridge is 20m above, and at right angles to, a river. A person in a train travelling at 60 km/h passes over the centre of the bridge at the same instant that a person in a motorboat travelling at 20km/h passes under the centre of the bridge. How fast are the two people separating 10s later?

sabrina_m33 · Mar 14, 2008

Please someone show me how to answer this!
Thanks!!

rocomath · Mar 14, 2008

Did you draw a picture? How does it look like?

Show your work plz!!!

sabrina_m33 · Mar 14, 2008

Only problem is I don't really know how to start!:(

rocomath · Mar 14, 2008

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?

sabrina_m33 · Mar 14, 2008

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

sabrina_m33 · Mar 14, 2008

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

sabrina_m33 · Mar 14, 2008

opps the answer is supose to be 62.8 km/h

rocomath · Mar 14, 2008

It asks you to evaluate it at 10s. You're rates have units km/h.

Convert hours to seconds.

sabrina_m33 · Mar 14, 2008

and I never rounded any if my numbers, stored them all in my calc.

sabrina_m33 · Mar 14, 2008

yes I did convert.. the 60 km/h goes to 166.66m/s and the 20km/h to 5.55m/s

rocomath · Mar 14, 2008

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.

sabrina_m33 · Mar 14, 2008

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!

rocomath · Mar 14, 2008

I got the same answer. Perhaps your teacher rounded off, who knows? Wouldn't worry too much.

sabrina_m33 · Mar 14, 2008

yeah maybe.. only problem is this is an assignment that's due for marks!!
Well thank you for your help!!:D

rocomath · Mar 14, 2008

Anytime, gl! Make 100s :)

sabrina_m33 · Mar 14, 2008

does the height of 20m have anything to do with the calculations?

ghostanime2001 · Oct 30, 2008

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 im using Advanced FUnctions and Introductory Calculus from Harcourt Mathematics 12 . Thats where u got this question from lol and no from ur teacher llllooool <_<