A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius of the outer ripple is increasing at a constant rate of 1 foot per second. When the radius is 4 feet, at what rate is the total area 𝐴 of the disturbed water changing? Duration: 4:56

Air is being pumped into a spherical balloon at a rate of 4.5 cubic feet per minute. Find the rate of change of the radius when the radius is 2 feet. Duration: 7:13

An airplane is flying on a flight path, at an altitude of 6 miles, that will take it directly over a radar tracking station. If the distance from the plane to the tracking station is decreasing at a rate of 400 miles per hour when that distance is 10 miles, what is the speed of the plane? Duration: 10:19

A 10-foot ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 feet from the wall? Duration: 6:24

A 10-foot ladder (from the previous Exercise) rests against a vertical wall. Let 𝜃 be the angle the ladder makes with the ground. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, what is the rate of change in 𝜃 when the bottom of the ladder is 6 feet from the wall? Duration: 9:27

A water tank has the shape of an inverted circular cone with a base radius of 2 m and a height of 4 m. If water is being pumped into the tank at a rate of 2 m^3/min, find the rate at which the water level is rising when the water is 3 m deep. Duration: 11:41

A BUG (Being of Unspecified Gender) walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 20 ft from the path and is kept focused on the BUG. At what rate is the searchlight rotating when the BUG is 15 ft from point on the path closest to the searchlight? Duration: 11:21