An airplane flying at an altitude of 6 miles passes directly

An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane is 10 miles away (s =10),the radar detects that the distance s is changing at a rate of 250 miles per hour. What is the speed of the airplane?

Solution

s^2=6^2+x^2 when s=10 x=8 differentiating wrt time 2sds/dt=2xdx/dt s(ds/dt)=x(dx/dt) 10(250)=8(dx/dt) v=dx/dt=312.5