Related Rates and Two Approaching Cars

In this video, we solve a related rates problem involving a two cars driving toward each other. It involves implicit differentiation of the Pythagorean equation. This examples involves three rates of change, two are known and one is unknown.

This lecture is based upon Section 3.9 of Calculus by James Stewart. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.

[Chan-vvlg]

At 5:55, you mentioned that since derivative is 50, we have to write 2xx'. I don't think I follow along quite well. Wouldn't the derivative of x^2 just be 2x? Thank you!

[javiergarcia-cuervavelasco]

Hi, great explanation!

How would you resolve the problem if the intersection angle is not 90°? But you know one other angle.

Deriving the trigonometry function sin x = opposite/hypotenuse, for instance?

I'm trying to calculate the time of impact of a torpedo in a ship, where we know the the distance between me, the submarine, and the ship, and we also know the angle made from the distance between us and in its direction (angle of bow).
I know it's trigonometry, and I can calculate the angle of the torpedo, but as the ship and the torpedo got a speed I think we have to derive by time to calculate when the torpedo will impact.