Related Rates: Police Car (Flawed Approach)

[starofdc]

why that must be the most beautifully depicted double decker police car I have ever observed with my binocular vision.

4:21 "Where do the wise go?" sounds like a philosophical question. (Yes, I know that that's not what was said.)

[johnnolen]

This approach is not as flawed as it seems. At t = 2 seconds, the instant you're interested in, x = 40, y = 120, and z = 40·sqrt[10]. If θ = Arctan (y/x) then the derivative of the outside function is 1/sec^2 (θ) = [40/(40·sqrt[10])]^2 = 1/10. By the quotient rule the derivative of the inside function is [y/x]' = (x·dy/dt - y·dx/dt) ÷ x^2 = (40 × 60 - 120 × - 80) ÷ 40^2 = 15/2. Therefore, dθ/dt = 1/10 × 15/2 = 15/20 = 3/4 ◼