3470.21 – Distance in flight

You and a friend each pilot a jet plane starting from the same spot in Michigan at exactly noon on a Thursday. You travel due east at xx kilometers per hour, and your friend travels due south at yy kilometers per hour. Use the Pythagorean Theorem to devise a formula for dd, the distance in kilometers between your two planes after tt hours of flight. Assume the two planes remain at the same height.

Solution

This is one of those problems where it helps a great deal to discard the useless information and simply draw a picture. Below is the one I made. Isn't it lovely? It suggests the following formulas:

d2=(xt)2+(yt)2,d^2 = (xt)^2 + (yt)^2,

d=t⋅x2+y2.d = t \cdot \sqrt{x^2 + y^2}.

3470_21_solution_55794911a4.png