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June 3rd, 2010, 09:11 AM   #1
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Related Rates Problem: Find rate that distance is changing.

A man walks north at 1.8m/s, a woman walks east at 2m/s. At what rate is the distance between them increasing after one minute if they leave from the same point at the same time.

Attempt @ Work:

dx/dt = 1.8m/s
dy/dt = 2m/s

Find dz/dt after 60 seconds.

I made a triangle.

60 * 1.8 = 108m/s
60 * 2 = 120m/s

Pythagorean Theorem

120^2 + 108^2 = z^2
z = ~161.44

x^2 + y^2 = z^2

Differentiate

2x * dx/dt + 2y * dy/dt = 2z * dz/dt

Replace variables in

[ 2(10(1.8 )+2(120)(2) ] / [2(161.44)] = 2.7
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June 3rd, 2010, 11:55 AM   #2
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Re: Related Rates Problem: Find rate that distance is changing.

Yep. That's what I get. Good show

Unless we're both wrong, but I don't think so.
 
June 5th, 2010, 04:34 AM   #3
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Re: Related Rates Problem: Find rate that distance is changing.

Nice work
It would be nice to visualize all this on an x-y plane
and it would be convenient to use dy/dt for the man moving north (along the y axis) and dx/dt for the woman moving east (along the x-axis)

I'm just saying.
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