Discussion:  All Lesson Plans in Calculus on TI Calculator 
Topic:  teacher needs help! 
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Subject:  RE: teacher needs help! 
Author:  Craig 
Date:  Dec 14 2004 
of Math Forum might be better), I'll take a stab at your problem. html won't be
pretty, but here goes:
D = D(t) = distance between car and truck,
N = N(t) = distance car is north of intersection
E = E(t) = distance truck is east of intersection.
By Pyth. Thm, D^2 = N^2 + E^2. Differentiating both sides implicitly gives
2D dD/dt = 2N dN/dt + 2E dE/dt
I'll switch to prime notation now (dD/dt = D'), and divide both sides by 2D to
get
D' = (N N' + E E')/D
After 2 hrs, N = 60*2 = 120; E = 45*2 = 90, and D = sqrt(120^2 + 90^2) = 150.
N' = 60 and E' = 45. Thus,
D' = (120 * 60 + 90 * 45)/150 = 75.
An alternative approach (I've seen many students who take physics concurrently
come up with this): N(t) = 60t, E(t) = 45t, so D(t) = 75t (the Pythagorean
triple), so "of course" dD/dt = 75.
 
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