Problems for "Related Rates"
Problem 2.1:
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?
[Solution]
Problem 2.2:
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?
[Solution]
Problem 2.3:
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?
[Solution]
Problem 2.4:
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?
[Solution]
