Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q76P (page 61)

A vectorB⇀, with a magnitude of8.0m, is added to a vector A⇀, which lies along an x axis. The sum of these two vectors is a third vector that lies along the y axis and has a magnitude that is twice the magnitude ofA⇀. What is the magnitude of A⇀?

Short Answer

Expert verified

The magnitude ofA⇀is3.6m

Step by step solution

01

To understand the concept

This problem is based on the triangle law of vector addition. In this law, when two vectors are represented by sides of the triangle taken in the same order of magnitude and direction, the resultant sum of these two vectors is given by the third vector. This concept can be used here to find the magnitude of vectorA⇀.

Using the above concept third vector C can be written as

C⇀=A⇀+B⇀

Given are,

B⇀=8.0m

02

To find the magnitude of A⇀

Here, vectorA⇀is along x ais, so the angle at A⇀is 0. The vectorC⇀lies along y axis, so the angle for C⇀is 90°.

Using Pythagorean theorem,

B=A2+C28.0m=A2+4A2A=85=3.6m

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

In a game of lawn chess, where pieces are moved between the centers of squares that are each 1.00m on edge, a knight is moved in the following way: (1) two squares forward, one square rightward; (2) two squares leftward, one square forward; (3) two squares forward, one square leftward. What are (a) the magnitude and (b) the angle (relative to “forward”) of the knight’s overall displacement for the series of three moves?

In a meeting of mimes, mime 1 goes through a displacementd→1=(4.00m)i⏜+(5.00m)j⏜and mime 2 goes through a displacementd→2=(-3.0m)i⏜+(4.0m)j⏜. What are (a) d→1×d→2, (b) d→1.d→2, (c) (d→1+d→2)d→2, and (d) the component ofd→1along the direction ofd→2? (Hint: For (d), see Eq.3-20and fig3-18.)

A sailboat sets out from the U.S. side of Lake Erie for a point on the Canadian side,90.0 km due north. The sailor, however, ends up 50.0 kmdue east of the starting point. (a) How far and (b) in what direction must the sailor now sail to reach the original destination?

You are to make four straight-line moves over a flat desert floor, starting at the origin of an xy coordinate system and ending at the xy coordinates (-140 m,30 m . The x component and y component of your moves are the following, respectively, in meters:(20 and 60) , then (bxand-70), then (-20 andsy) , then (-60 and -70) . What are (a) component and (b) component ? What are (c) the magnitude and (d) the angle (relative to the positive direction of the x axis) of the overall displacement?

For the displacement vectors a→=(3.0m)i⏜+(4.0m)j⏜and b→=(5.0m)i⏜+(-2.0m)j⏜, give a→+b→in (a) unit-vector notation, and as (b) a magnitude and (c) an angle (relative to i⏜). Now give b→-a→in (d) unit-vector notation, and as (e) a magnitude and (f) an angle.
See all solutions

Recommended explanations on Physics Textbooks

Wave Optics

Read Explanation

Atoms and Radioactivity

Read Explanation

Fundamentals of Physics

Read Explanation

Force

Read Explanation

Solid State Physics

Read Explanation

Thermodynamics

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