An airplane is flying on a compass heading (bearing) of 170° at 460 mph. A wind is blowing with the bearing 200° at 80 mph. a. Find the component form of the velocity of the airplane. b. Find the actual ground speed and direction of the airplane.
An airplane is flying on a compass heading (bearing) of 170° at 460 mph. A wind is blowing with the bearing 200° at 80 mph. a. Find the component form of the velocity of the airplane. b. Find the actual ground speed and direction of the airplane.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
PLEASE ANSWER IN AN EASY TO READ FORMAT!!!! PLEASE AND THANK YOU!!!! Make sure to answer all parts of the question.
![### 2. Part 2 - Find the error(s) and solve the problem correctly.
An airplane is flying on a compass heading (bearing) of 170° at 460 mph. A wind is blowing with the bearing 200° at 80 mph.
#### Questions:
a. Find the component form of the velocity of the airplane.
b. Find the actual ground speed and direction of the airplane.
#### Answer:
a. The velocity vector \( v \) of the airplane is calculated using its speed and direction:
\[
v = 460 \times \langle \cos 170^\circ, \sin 170^\circ \rangle = \langle -453.01, 79.88 \rangle
\]
b. Next, determine the wind vector \( w \) using its speed and direction:
\[
w = 80 \times \langle \cos 200^\circ, \sin 200^\circ \rangle = \langle -75.18, -27.36 \rangle
\]
Add the airplane's velocity vector \( v \) and the wind vector \( w \) to find the resultant velocity vector \( v + w \):
\[
\text{Velocity vector} = v + w = \langle -528.19, 52.52 \rangle
\]
Calculate the actual speed (ground speed) by finding the magnitude of the resultant velocity vector:
\[
\text{Actual speed} = \| v + w \| = \sqrt{(-528.19)^2 + (52.52)^2} \approx 530.79 \text{ mph}
\]
Determine the actual direction \( \theta \), noting that an angle larger than 180° is used:
\[
\text{Actual direction:} \ \theta = 180^\circ + \tan^{-1} \left( \frac{-528.19}{52.52} \right) = 95.68^\circ
\]
These steps outline the procedure to calculate the component form of the airplane's velocity, and subsequently, the actual ground speed and direction considering wind influence. The process involves vector addition and trigonometric functions to resolve the movement vectors accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feeea96f9-d9e2-4e41-9df9-d54882930b66%2F29b4b561-0835-4a14-8229-218562c9fccd%2Fl99osr8_processed.png&w=3840&q=75)
Transcribed Image Text:### 2. Part 2 - Find the error(s) and solve the problem correctly.
An airplane is flying on a compass heading (bearing) of 170° at 460 mph. A wind is blowing with the bearing 200° at 80 mph.
#### Questions:
a. Find the component form of the velocity of the airplane.
b. Find the actual ground speed and direction of the airplane.
#### Answer:
a. The velocity vector \( v \) of the airplane is calculated using its speed and direction:
\[
v = 460 \times \langle \cos 170^\circ, \sin 170^\circ \rangle = \langle -453.01, 79.88 \rangle
\]
b. Next, determine the wind vector \( w \) using its speed and direction:
\[
w = 80 \times \langle \cos 200^\circ, \sin 200^\circ \rangle = \langle -75.18, -27.36 \rangle
\]
Add the airplane's velocity vector \( v \) and the wind vector \( w \) to find the resultant velocity vector \( v + w \):
\[
\text{Velocity vector} = v + w = \langle -528.19, 52.52 \rangle
\]
Calculate the actual speed (ground speed) by finding the magnitude of the resultant velocity vector:
\[
\text{Actual speed} = \| v + w \| = \sqrt{(-528.19)^2 + (52.52)^2} \approx 530.79 \text{ mph}
\]
Determine the actual direction \( \theta \), noting that an angle larger than 180° is used:
\[
\text{Actual direction:} \ \theta = 180^\circ + \tan^{-1} \left( \frac{-528.19}{52.52} \right) = 95.68^\circ
\]
These steps outline the procedure to calculate the component form of the airplane's velocity, and subsequently, the actual ground speed and direction considering wind influence. The process involves vector addition and trigonometric functions to resolve the movement vectors accurately.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 13 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON