Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 17

Making a turn, a jetliner flies \(2.1 \mathrm{km}\) on a circular path of radius \(3.4 \mathrm{km} .\) Through what angle does it turn?

Short Answer

Expert verified
The jetliner turns through an angle of approximately 35.4 degrees.

Step by step solution

01

Understand the given information

We start by understanding the information given in the problem. A jetliner makes a turn and flies \(2.1 \mathrm{km}\) along a circular path with a radius of \(3.4 \mathrm{km} .\)
02

Conversion of units

For convenience of calculation, convert the distances from kilometers to meters.
03

Derive the formula to find the angle subtended

The formula to find the angle subtended at the center of the circle by a given arc length and radius is \( \theta = \frac{s}{r} \). In this case, \( \theta \) is the angle in radians we are trying to find, \( s \) is the length of the arc which is 2100 meters, and \( r \) is the radius of the circle which is 3400 meters.
04

Apply the values into the formula

Now apply these values into the formula to get \( \theta = \frac{2100}{3400} = 0.6176 \) radians.
05

Convert the answer to degrees

As the question asks for the angle in degrees, convert the answer from radians to degrees by using the formula \( \Theta(degrees) = \Theta(radians) \times \frac{180}{\pi} .\) Hence, the answer is \(0.6176 \times \frac{180}{\pi} = 35.4 \) degrees (rounded to one decimal place).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

When we write the number 3.6 as typical of a number with two significant figures, we're saying that the actual value is closer to 3.6 than to 3.5 or \(3.7 ;\) that is, the actual value lies between 3.55 and \(3.65 .\) Show that the percent uncertainty implied by such twosignificant-figure precision varies with the value of the number, being the lowest for numbers beginning with 9 and the highest for numbers beginning with \(1 .\) In particular, what is the percent uncertainty implied by the numbers (a) \(1.1,\) (b) \(5.0,\) and (c) \(9.9 ?\)

since the start of the industrial era, humankind has emitted about half an exagram of carbon to the atmosphere. What's that in tonnes \((t ; 1 t=1000 \mathrm{kg}) ?\)

A car is moving at \(35.0 \mathrm{mi} / \mathrm{h}\). Express its speed in (a) \(\mathrm{m} / \mathrm{s}\) and (b) \(\mathrm{ft} / \mathrm{s}\).

A year is very nearly \(\pi \times 10^{7}\) s. By what percentage is this figure in error?

In the 1908 London Olympics, the intended 26 -mile marathon was extended 385 yards to put the end in front of the royal reviewing stand. This distance subsequently became standard. What's the marathon distance in kilometers, to the nearest meter?
See all solutions

Recommended explanations on Physics Textbooks

Radiation

Read Explanation

Oscillations

Read Explanation

Quantum Physics

Read Explanation

Solid State Physics

Read Explanation

Classical Mechanics

Read Explanation

Electric Charge Field and Potential

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free