Related Rates 1. Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm3 /s. How fast is the radius of the balloon increasing when the diameter is 50 cm? 2. A ladder 10 ft long 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 ft from the wall? 3. Jeb is traveling west at 50 mi/h and Zeb is traveling north at 60 mi/h. Both are headed for the intersection of the two roads. At what rate are the cars approaching eachother when Jeb is 0.3 mi and Zeb is 0.4 mi from the intersection? 4. A New Mexican Whooping Llama walks along a straight path at a speed of 4 ft/s. A searchlight (gotta keep an eye on those whooping llamas!) is located on the ground 20 ft from the path and is kept focused on the llama. At what rate is the searchlight rotating when the llama is 15 ft from the point of the path closest to the searchlight? 5. A water tank has the shape of an inverted circular cone with base radius 2 m and height 4 m. If water is being pumped into the tank at a rate of 2 m3 /min, find the rate at which the water level is rising when the water is 3 m deep. 6. A 5-ft tall orangutan named Harold walks at 8 ft/s toward a street light that is 20 ft above the ground. What is the rate of change of the length of Harold’s shadow when he is 15 feet from the street light? At what rate is the tip of his shadow moving? 7. A landscape light at ground level lights up the side of a tall building that is 15 feet from the light. A 6-ft tall orangutan named Maude starts walking from the light directly toward the building. How fast is she walking when she is 9 feet from the light and if her shadow is decreasing at a rate of 2 ft/s at that instant?
