/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 40 A meteorologist for a TV station... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 20: Problem 40

A meteorologist for a TV station is using radar to determine the distance to a cloud. He notes that a time of \(0.24 \mathrm{~ms}\) elapses between the sending and the return of a radar pulse. How far away is the cloud?

Short Answer

Expert verified
The cloud is 36,000 meters away.

Step by step solution

01

Understanding the Problem

We need to determine the distance to a cloud using radar. A radar pulse is sent and returns after 0.24 ms (milliseconds). Our task is to calculate the distance to the cloud based on this time.
02

Understanding Radar Function

The radar sends out a pulse that travels to the cloud and then returns. The total travel time is the time the radar pulse takes to go to the cloud and back to the radar.
03

Convert Time to Seconds

Since the problem gives the time in milliseconds, we need to convert this to seconds. Since 1 millisecond (ms) is equal to 0.001 seconds, we multiply 0.24 ms by 0.001 to get the time in seconds: \(0.24 \times 0.001 = 0.00024\) seconds.
04

Calculate the One-Way Time

The measured time includes the trip to the cloud and back, so we need the one-way travel time to calculate the distance. Divide it by 2: \(0.00024 \text{ sec} \div 2 = 0.00012 \text{ sec}\).
05

Using the Speed of Light

Radar waves travel at the speed of light, which is approximately \(3 \times 10^8\) meters per second. We use this speed to calculate the distance based on the one-way travel time.
06

Calculate the Distance to the Cloud

Multiply the one-way travel time by the speed of light to find the distance to the cloud: \(\text{Distance} = \text{Speed of Light} \times \text{One-Way Time} = 3 \times 10^8 \times 0.00012 \text{ seconds}\).
07

Perform the Calculation

Calculate the distance:\(\text{Distance} = 3 \times 10^8 \times 0.00012 = 36,000 \text{ meters}\).

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Radar Technology
Radar technology is an essential tool for detecting objects and measuring distances. It works by sending out a pulse of radio waves, which travel through the air and reflect off objects. The radar detects the reflected waves and uses the time it takes for the waves to return to calculate the distance of the object.
  • Radar systems consist of a transmitter, which sends the pulse, and a receiver, which picks up the reflection.
  • The time delay between sending and receiving the pulse is crucial because it indicates how far the object is from the radar.
In meteorology, radar is commonly used to measure distances to clouds and analyze weather patterns. This technology helps meteorologists predict weather changes by providing real-time data about the distance and movement of clouds.
Speed of Light
The speed of light is a fundamental constant in physics, represented by the symbol "c". It is approximately valued at \(3 \times 10^8\) meters per second. Light, including radar waves, travels at this speed in a vacuum, providing a constant reference point for measuring distances. Understanding the speed of light is crucial because:
  • It allows for precise calculations of distances based on time measurements.
  • This speed is constant in vacuum, making it a reliable standard for various technologies, especially in air or space applications.
In radar technology, knowing that the radar waves travel at the speed of light means that you can accurately determine distances by measuring the time it takes for the pulse to travel to an object and back.
Distance Calculation
Distance calculation using radar involves determining how far an object is based on how long it takes for a radar pulse to bounce back. This process uses the relationship between speed, time, and distance in the formula:\[\text{Distance} = \text{Speed} \times \text{Time}\]In our case, since the radar pulse travels to the cloud and back, we first calculate the one-way distance by halving the total travel time.
  • The measured time is divided by two to get the one-way travel time, which is needed for the equation.
  • Multiply this one-way time by the speed of light to get the distance.
This calculation provides an accurate measure of how far the cloud, or any other object detected by radar, is from the radar source.
Unit Conversion
Unit conversion is a key step in solving problems involving different measurements. In our radar problem, we initially have the time measured in milliseconds (ms), but to use the formula for distance, we need this time in seconds. To convert time from milliseconds to seconds:
  • Understand that 1 millisecond equals 0.001 seconds.
  • Multiply the number of milliseconds by 0.001 to get the time in seconds.
For example, a time of 0.24 milliseconds is converted to 0.00024 seconds by multiplying by 0.001. Converting units correctly ensures that calculations using physical constants, like the speed of light, are accurate and meaningful.

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

A \(240-\mathrm{V}\) dc motor has an armature whose resistance is \(1.50 \Omega\). When running at its operating speed, it draws a current of 16.0 A. (a) What is the back emf of the motor when it is operating normally? (b) What is the starting current? (Assume that there is no additional resistance in the circuit.) (c) What series resistance would be required to limit the starting current to \(25 \mathrm{~A} ?\)

The secondary coil of an ideal transformer has 450 turns, and the primary coil has 75 turns. (a) Is this transformer a (1) step-up or (2) step-down transformer? Explain your choice. (b) What is the ratio of the current in the primary coil to the current in the secondary coil? (c) What is the ratio of the voltage across the primary coil to the voltage in the secondary coil?

A uniform magnetic field is at right angles to the plane of a wire loop. If the field decreases by \(0.20 \mathrm{~T}\) in \(1.0 \times 10^{-3} \mathrm{~s}\) and the magnitude of the average emf induced in the loop is \(80 \mathrm{~V},\) (a) what is the area of the loop? (b) What would be the value of the average induced emf if the field change was the same but took twice as long to decrease? (c) What would be the value of the average induced emf if the field decrease was twice as much and it also took twice as long to change?

An ideal solenoid with a current of 1.5 A has a radius of \(3.0 \mathrm{~cm}\) and a turn density of 250 turns \(/ \mathrm{m}\). (a) What is the magnetic flux (due to its own field) through only one of its loops at its center? (b) What current would be required to double the flux value in part (a)?

In \(0.20 \mathrm{~s}\), a coil of wire with 50 loops experiences an average induced emf of \(9.0 \mathrm{~V}\) due to a changing magnetic field perpendicular to the plane of the coil. The radius of the coil is \(10 \mathrm{~cm}\), and the initial strength of the magnetic field is 1.5 T. Assuming that the strength of the field decreased with time, (a) what is the final strength of the field? (b) If the field strength had, instead, increased, what would its final value have been? (c) Explain a method whereby you could, in principle, tell whether the field was increasing or decreasing in magnitude.
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Electromagnetism

Read Explanation

Geometrical and Physical Optics

Read Explanation

Scientific Method Physics

Read Explanation

Physics of Motion

Read Explanation

Circular Motion and Gravitation

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.