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Stationary Person
We want to find at what rate (measured in ft/min) the distance between the two people is changing when
$\theta = 0.3$ radians.
What are we trying to find here?
$\frac{dx}{dt}$
$\frac{d\theta}{dt}$
$\frac{dd}{dt}$
$\frac{d\theta}{dx}$
$\frac{dr}{dt}$
$\frac{dz}{dt}$
To get us started, write an equation from the triangle and isolate the length $z$. The answer should involve
the angle $\theta$.
Answer: $41 \sec(\theta)$
Now, we were told that initially, the two people were standing on the same horizontal line, which means
that initially, the angle $\theta$ was zero. What is $\theta$ as a function of time, $t$?
Answer: $\theta = \frac{t}{41}$
Now take the expression we wrote above for $z$ and rewrite it as a function of time, $t$.
Answer: $z = $
