AP Calculus AB
Homework: Related Rates Worksheet #1
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1. Romeo is climbing up to Juliet’s balcony on a 25 ft. ladder which leans against a vertical wall of
her castle. Juliet wants to play “hard to get” and pushes the top of the ladder towards the
ground. If the bottom of the ladder slides away from the castle at a rate of 4 ft/sec:
a) How fast is Romeo sliding down the wall of the castle when the top of the ladder is 15 ft
above the ground?
b) How fast is the angle between the ground and the ladder changing at the same instant?
2. Bernard and Bertha go out for a romantic dinner. They order a bottle of wine, so the waiter
brings them conical glasses which have an altitude of 4 inches and a diameter of 3 inches. If
the wine is poured into a glass at a rate of 15 in3/min., find the rate at which the wine level is
rising when the wine is halfway up to the top of the glass.
3. Winnie the Pooh lost his honey in the Hundred Acre Woods. Eeyore volunteers to help Pooh in
his search. They start at a bridge. Pooh stumbles north at a rate of 2 ft/sec. Eeyore waddles
west at a rate of 3 ft/sec. At what rate is the distance between Pooh and Eeyore changing after
they have been searching for 25 minutes?
4. A young girl has spent the day gathering rice. Unfortunately, there is a hole in the bottom of
her sack, so the rice leaks out forming a conical pile with a constant altitude of 8 inches and a
radius changing at a rate of 4 in/min. What is the rate of change of the volume of the pile when
the volume is 1400 in3 ?
5. Bonzo the clown wants the volume of a balloon to increase at a rate of 25 in3/sec. At what rate
would the radius change when the diameter of the balloon is 4 inches?
6. A balloon is rising vertically above a level, straight road at a constant rate of 1 ft/sec. Just when
the balloon is 65 feet above the ground, a bicycle passes under it, going 17 ft/sec. How fast is
the distance between and bicycle and the balloon changing 3 seconds later?
7. A policeman chases a getaway car of bank robbers. The getaway car takes a sharp turn and
heads north at a rate of 125 mph. The police car is unable to react and is forced to continue
east in a straight path at a rate of 100 mph.
a) After 10 seconds, how far apart are the 2 cars?
b) What is the rate of change of the distance between the 2 cars (to the nearest mph)?
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