Homework Help is Here – Start Your Trial Now!
Math
Calculus
Q8: If L = 100, h = 6, and v0 = 450mph, sketch a graph of dy/dt. What does this tell us about vertical velocity along the flight path?

Q8: If L = 100, h = 6, and v0 = 450mph, sketch a graph of dy/dt. What does this tell us about vertical velocity along the flight path?

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.CT: Test
Problem 22CT
See similar textbooks
icon
Related questions
Question

Q8: If L = 100, h = 6, and v0 = 450mph, sketch a graph of dy/dt. What does this tell us about vertical velocity along the flight path?

In this project we will analyze the flight path and velocity of an airplane making a landing. We assume the plane is at an altitude of h miles, and is L miles horizontally from the airport. Let's place the airport at the origin and the plane at position (-L, h) as shown. We will call the actual flight path y(x). 1. If we want the flight path to be horizontal at the beginning and horizontal at landing, we have four mathematical conditions that our function y(x) must satisfy. Write those conditions here. To help you get started I've written out the first two conditions (at the beginning of landing), but you need to finish writing out the other two: y(-L) = h y'(-L) = 0 y(0) = 0 y'(0) = 0
Transcribed Image Text:In this project we will analyze the flight path and velocity of an airplane making a landing. We assume the plane is at an altitude of h miles, and is L miles horizontally from the airport. Let's place the airport at the origin and the plane at position (-L, h) as shown. We will call the actual flight path y(x). 1. If we want the flight path to be horizontal at the beginning and horizontal at landing, we have four mathematical conditions that our function y(x) must satisfy. Write those conditions here. To help you get started I've written out the first two conditions (at the beginning of landing), but you need to finish writing out the other two: y(-L) = h y'(-L) = 0 y(0) = 0 y'(0) = 0
3. So let's try a cubic function: y(x) = ax3 + bx² + cx + d. Apply the four conditions you have 3h above to demonstrate that y(x) = 2h 3 +2 is the correct cubic equation. This will require some careful solving, but perhaps first start by applying the conditions at the origin. 4. Graph this function with L = 100 and h = 6 to confirm the shape. Draw this graph below. Be sure to set your domain from -L<x < 0. 5. For L = 100 and h = 6, calculate lip What are the units of this answer? Is this the plane's dx velocity? Next, evaluate dy dr r=-50. Be sure to include units on your answer! 2/4 6. The function y(x) gives us the shape of the flight path, but doesn't tell us about time or dy dr dx dt speed. Explain why the expression where t is time in hours, really can be thought of dy ,or the plane's vertical velocity. as dt da dy in terms of x (and h and L). dt 7. If is a constant vo, find a general expression for dt
Transcribed Image Text:3. So let's try a cubic function: y(x) = ax3 + bx² + cx + d. Apply the four conditions you have 3h above to demonstrate that y(x) = 2h 3 +2 is the correct cubic equation. This will require some careful solving, but perhaps first start by applying the conditions at the origin. 4. Graph this function with L = 100 and h = 6 to confirm the shape. Draw this graph below. Be sure to set your domain from -L<x < 0. 5. For L = 100 and h = 6, calculate lip What are the units of this answer? Is this the plane's dx velocity? Next, evaluate dy dr r=-50. Be sure to include units on your answer! 2/4 6. The function y(x) gives us the shape of the flight path, but doesn't tell us about time or dy dr dx dt speed. Explain why the expression where t is time in hours, really can be thought of dy ,or the plane's vertical velocity. as dt da dy in terms of x (and h and L). dt 7. If is a constant vo, find a general expression for dt
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Differential Equation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS