Derivatives - chain rule

Question

An airplane, flying horizontally at an altitude of 1 mile, passes directly over an observer. If the constant speed of the airplane is 400 miles per hour, how fast is its distance from the observer increasing 45 seconds later? Hint: note that in 45 seconds (3/4 * 1/60 = 1/80), the airplane goes 5 miles.

Answer 1

the distance z is found using

z^2 = 1^2 + x^2
at x=5, z^2 = 26

z dz/dt = x dx/dt

so at the moment in question

√26 dz/dt = 5*400

note that z will be in mi/hr