# Calculus AB: Applications of the Derivative

### Problems for "Related Rates"

Problem : David and Angela start at the same point. At time t = 0 , Angela starts running 30ft/sec north, while David starts running 40ft/sec east. At what rate is the distance between them increasing when they are 100 feet apart?

Problem : Sophia is sitting on the ground 10 feet from the spot where a hot air balloon is about to land. She is watching the balloon as it travels at a steady rate of 20 feet per second towards the ground. If θ is the angle between the ground and her line of sight to the balloon, at what rate is this angle changing at the instant the balloon hits the ground?

Problem : Indy is 6 feet tall and is walking at a rate of 3 feet per second towards a lamppost that is 18 feet tall. At what rate is his shadow due to the lamppost shortening when he is 6 feet from the base of the lamppost?

Problem : Water is being poured into an inverted cone (has the point at the bottom) at the rate of 4 cubic centimeters per second. The cone has a maximum radius of 6cm and a height of 30 cm. At what rate is the height increasing when the height is 3cm?

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