Chapter 3.4, Problem 34ES

An aircraft is flying at a constant altitude with a constant speed of $600\text{ mi/h}$ . An antiaircraft missile is fired on a straight line perpendicular to the flight path of the aircraft so that it will hit the aircraft at a point $P$ (see the accompanying figure). At the instant the aircraft is $2\text{ mi}$ from the impact point $P$ the missile is $4\text{ mi}$ from $P$ and flying at $1200\text{ mi/h}$ . At that instant, how rapidly is the distance between missile and aircraft decreasing?