Question

A plane travels east from San francisco towards St. Louis at 500 miles per hour, and a turbojet travels north from new orleans toward St. louis at 600 miles per hour. Find the rate of change of the distance between them when the jets are 300 miles apart, and the plane is 100 miles from St. Louis.

Answer 1

Let the plane be x west, and the jet be y south of St. Louis.

Draw a diagram. Then the distance z between the two aircraft is

z^2 = x^2+y^2
At the moment in question,
300^2 = 100^2+y^2
y = 100√8

z dz/dt = x dx/dt + y dy/dt
300 dz/dt = 100(-500) + 100√8 (-600)
dz/dt ≈ -732 mi/hr