Question

REALATED RATES = Two commercial jets at 40,000 ft. are both flying at 520 mph towards an airport. Plane A is fliyinh south and is 50 miles from the airport while Plane B is flying west and is 120 miles from the airport. How fast is the distance between the two planes changing at this time?

Answer 1

you know by pythagoras that
\[x^2+y^2=z^2\] taking derivatives gives you
\[2xx'+2yy'=2zz'\] or
\[xx'+yy'=zz'\] and you are told that
\[x'=y'=520\] and also that
\[x=50,y=120\] solve for z using the pythagoras and plug in the numbers to find z'