# AP Calculus Related Rates

An airplane is flying at an altitude of 7 miles and passes directly over a radar antenna as shown in the figure. When the plane is 10 miles from the antenna, the radar detects that the distance between the plane and the tower is changing at the rate of 300 mph. What is the speed of the airplane at that moment?

## Related Problems

A 20 foot ladder is leaning against a wall and the base of the ladder is sliding away at 6 feet a second. How fast is the top of the ladder sliding down the wall when the base of the ladder is 12 feet from the wall?

Let $y = 2(x^2 - 3x)$

a. Find $\frac{dy}{dt}$ when $x = 3$ given $\frac{dx}{dt} = 2$

b. Find $\frac{dx}{dt}$ when $x = 1$ given $\frac{dy}{dt} = 5$

Let $y = \sin{(x)}$

Find $\frac{dy}{dt}$ when $x = \frac{\pi}{4}$ given $\frac{dx}{dt} = 2 \frac{cm}{sec}$

A 10 by 6 foot rectangular swimming pool is being filled. Find the rate at which the height of the water rises if the hose is pouring at $20 \frac{{ft}^3}{hour}$