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Chapter 3: Q76P (page 61)

A vectorB鈬赌, with a magnitude of8.0m, is added to a vector A鈬赌, 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鈬赌. What is the magnitude of A鈬赌?

Short Answer

Expert verified

The magnitude ofA鈬赌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鈬赌.

Using the above concept third vector C can be written as

C鈬赌=A鈬赌+B鈬赌

Given are,

B鈬赌=8.0m

02

To find the magnitude of A⇀

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

Using Pythagorean theorem,

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

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