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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

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