I've been going through my notes and can't find any info on this so I'm hoping there is someone out there who knows how to do this!
Calculus Question
Consider the line in the x,y - plane given by the equation y=2.2x - 1.9
x and y are both in km
Suppose Jim starts at the point on the curve where x = 0
Jim walks (approx) North East along the line at a rate of 6.2km/hr
1. Parametrize the line based on distance traveled (s).
2. Parametrize the line based on time traveled (t).
Thanks for the help guys!
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Answers & Comments
Verified answer
1) Parametrize the line based on distance traveled (s).
I think this is to find
x =f(s) and y =g(s) where f and g are functions of s
the simplest solution is
x = s
y = 2.2s - 1.9
2) This is easy if you know that dx/dt = v
then x = integral vdt = integral (6.2 dt) = 6.2 t + xo (1)
Now when t =0 then x = 0
Substitute into (1)
0 = 6.2 * t + xo = 6.2 * 0 +xo ==> xo = 0
then x = 6.2t
Substitute into y=2.2x - 1.9 then y =13.64 t - 1.9
Then x = 6.2t and y =13.64 t - 1.9
is the solution for #2