Question

A loon flying horizontally at an altitude of 3 meters and speed of 8 m/s passes over a turtle standing on the ground. Find the rate at which the distance between them is changing when they are 5 meters apart

Answer 1

Use \[
z^2 = x^2 + y^2
\]In this case \(y=3\) and \(y'=0\)

Answer 2

Implicit differentiation gives you: \[
2zz' = 2xx'
\]We also know that \(x' = 8\)

Answer 3

Also \(z=5\) and they want you to find \(z'\)

Answer 4

\(x\) by Pythagorean theorem is just: \(\sqrt{5^2-3^2}\)

Answer 5

@Mer94 Get it?