Subject: aircraft vs. missile Name: sarah Who are you: Student an aircraft is flying at a constant altitude with a constant speed of 600mph. 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. at that instant the aircraft is 2 miles from the impact point P the missile is 4 miles from P and flying at 1200 mph. at that instant, how rapidly is the distance between missile and aircraft decreasing? Hi Sarah. Because of the perpendicular, you should be able to draw this as a right triangle. The two legs are 2 miles (p=plane) and 4 miles (m=missile). The hypotenuse is given by Pythagoras' theorem. The hypotenuse is the distance between the plane and missile. h2 = p2 + m2 You are asked for the instantaneous rate of change of h, that is, dh/dt. So take the derivative of both sides: d/dt (h2) = d/dt (p2 + m2) If you work carefully and apply the chain rule where you need to, you will get an expression with dh/dt in it (you should solve for this, since that is what you are trying to find), h, m, p (all of which you know or can calculate from the pythagorean theorem), and dm/dt and dp/dt which are the speeds of the missile and plane. Plug in the values and find the value of dh/dt. Hope this helps, Stephen La Rocque.