CramX
RegisterLog in
Back to AI Flashcard MakerMathematics /AP Calculus AB: 7.4.4 The Blimp Problem

AP Calculus AB: 7.4.4 The Blimp Problem

Mathematics7 CardsCreated 3 months ago

This content presents related rate problems involving motion along right triangles, such as a blimp tied to a rope and a golf ball in flight. It demonstrates how to apply the Pythagorean theorem and implicit differentiation to find changing distances and angles, including the rate of change between clock hands and the angle of elevation during projectile motion.

PrintEmbedImportReport

The Blimp Problem

  • Related rate problems involve using a known rate of change to find an associated rate of change.

  • Use implicit differentiation when you cannot write the dependent variable in terms of the independent variable.

Tap or swipe ↕ to flip
Swipe ←→Navigate
1/7

Key Terms

Term
Definition

The Blimp Problem

  • Related rate problems involve using a known rate of change to find an associated rate of change.

  • Use implicit differentiatio...

note

  • A blimp traveling overhead is tied to a rope. The rope is let out at a rate of 3 feet per second.

  • Assuming the blimp remains...

Suppose that a certain clock has a minute hand that is 4 inches long and an hour hand that is 3 inches long. What is the rate of change of the distance between the tips of the minute and hour hands at 2:00?

−16.6 inches / hour

Laura is hitting a golf ball at the driving range. Suppose that the altitude of the ball is given in feet by the equation y = 200t − 40t ^2, where t is the time in seconds after she hits the ball. Suppose also that the horizontal velocity of the ball is constant and equal to 80 feet per second. At what rate is the angle of elevation of the ball changing 2 seconds after Laura hits the ball?

−0.15 radians / second

Two cars leave an intersection at the same time, one headed west and the other north. The westbound car is moving at 40 mph and the northbound car is moving at 50 mph. Fifteen minutes later, what is the rate of change in the perimeter of the right triangle created using the two cars and the intersection?

154.02 mph

An object is moving along the graph of the curve x^2y^2/2x−y=1. At a particular moment, the particle is at (1,1) and dx/dt=5. Find the value of dy/dt at this moment.

0

Log in to view all terms

Related Flashcard Decks

Mathematics

Essential SAT Math Formulas

This deck covers key formulas and concepts essential for the SAT Math section, including slope, distance, and vertex forms.

10 cards
View Deck
Mathematics

Algebra 1 Unit 1 Mastery Test

These properties of equality help maintain balance in an equation when performing the same operation on both sides. Inverse operations, like using addition to undo subtraction, are key tools in solving equations.

29 cards
View Deck
Mathematics

ATI TEAS Test Practice Mathematics Part 2

This flashcard set includes a variety of practical math questions covering percentages, conversions, averages, scale drawings, and basic algebra. It’s designed to strengthen problem-solving skills for real-life and standardized test situations.

53 cards
View Deck
Mathematics

ATI TEAS Test Practice Mathematics Part 1

This flashcard set includes a variety of practical math questions covering percentages, conversions, averages, scale drawings, and basic algebra. It’s designed to strengthen problem-solving skills for real-life and standardized test situations.

55 cards
View Deck
Mathematics

Unit 2 Progress Check: MCQ Part A

To determine the point where the tangent line to the graph of the function 𝑓f has a slope of 2 for 𝑥 >0 x>0, we use the fact that the slope of the tangent line at any point is given by the derivative 𝑓′(𝑥)f′(x).

15 cards
View Deck
Mathematics

Customary Liquid Measurement Units

This set of flashcards outlines key relationships between customary units of liquid measurement, including pints, cups, quarts, and gallons. It provides conversion facts to help understand how these units relate to one another in the U.S. measurement system.

3 cards
View Deck

Study Tips

  • Press F to enter focus mode for distraction-free studying
  • Review cards regularly to improve retention
  • Try to recall the answer before flipping the card
  • Share this deck with friends to study together
AP Calculus AB: 7.4.4 The Blimp Problem
TermDefinition

The Blimp Problem

  • Related rate problems involve using a known rate of change to find an associated rate of change.

  • Use implicit differentiation when you cannot write the dependent variable in terms of the independent variable.

note

  • A blimp traveling overhead is tied to a rope. The rope is let out at a rate of 3 feet per second.

  • Assuming the blimp remains at a constant altitude of 800 feet, how fast is the blimp moving when 100 feet of rope have been let out?

  • This situation can be modeled by a right triangle. Notice that it is not important to keep your diagram to scale. In fact, drawing to scale might mislead you, giving you false information.

  • The Pythagorean theorem relates the lengths of the sides of a right triangle to each other.

  • Use implicit differentiation to find the derivative of b with respect to time. Then substitute the known values into the equation.

Suppose that a certain clock has a minute hand that is 4 inches long and an hour hand that is 3 inches long. What is the rate of change of the distance between the tips of the minute and hour hands at 2:00?

−16.6 inches / hour

Laura is hitting a golf ball at the driving range. Suppose that the altitude of the ball is given in feet by the equation y = 200t − 40t ^2, where t is the time in seconds after she hits the ball. Suppose also that the horizontal velocity of the ball is constant and equal to 80 feet per second. At what rate is the angle of elevation of the ball changing 2 seconds after Laura hits the ball?

−0.15 radians / second

Two cars leave an intersection at the same time, one headed west and the other north. The westbound car is moving at 40 mph and the northbound car is moving at 50 mph. Fifteen minutes later, what is the rate of change in the perimeter of the right triangle created using the two cars and the intersection?

154.02 mph

An object is moving along the graph of the curve x^2y^2/2x−y=1. At a particular moment, the particle is at (1,1) and dx/dt=5. Find the value of dy/dt at this moment.

0

A spherical balloon is being inflated from a compressor. Suppose the volume of the balloon is increasing at a constant rate of 10 cubic inches per second. At what rate is the surface area of the balloon increasing when its radius is 6 inches?

3.3 square inches per second