A few days ago
Roger

Related rates calculus problem, can you help me please?

Hello I am having great difficulty with the following problem. If someone could solve it and show step by step soultion that would be easy for me to understand : ) I would be very appreciatve. Thank you.

A plane at an altitude of 1 mile is flying horizontally at 500miles/hr. It passes a radar station on the ground. What is the rate of change of the distance of the plane from the radar station when the plane has moved 2 miles?

Top 1 Answers
A few days ago
hayharbr

Favorite Answer

If you draw it as a right triangle, one leg is 1, one is 500t, and the hypotenuse is x, the distance between them. So you want dx/dt

x = sqrt (1^2 + (500t)^2) = (1 + 250000t^2)^1/2

Let u = 1 + 250000t^2, du/dt = 500000t

x = u^1/2, dx/du = 1/2 u ^ -1/2 or 1/2 times 1/sqrt u

dx/dt = dx/du times du/dt

= 1/2 times 1/ sqrt (1 +250000t^2 ) times 500000t

2 miles only takes 2/500 hours so plug 2/500 (0.004) in for t

0