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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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Most popular questions from this chapter

Vectors A鈫� and B鈫� lie in an xy plane. A鈫� has magnitude 8.00 and angle 130掳; has components localid="1657001111547" Bx=-7.72and By=9.20. What are the angles between the negative direction of the y axis and (a) the direction of A鈫�, (b) the direction of the product A鈫�脳B鈫�, and (c) the direction of localid="1657001453926" A鈫�脳(B鈫�+3.00)k铃�?

Vector A鈫�has a magnitude of6.00units, vectorB鈫�has magnitude of7.00units, andA鈫�.B鈫�has a value of14.0What is the angle between the directions of A鈫�and B鈫�?

Here are two vectors:

a鈫�=(4.00m)i铃�-(3.00m)j铃�b鈫�=(6.00m)i+(8.00m)j

What are (a) the magnitude and (b) the angle (relative to i ) of a鈫�? What are (c) the magnitude and (d) the angle of b鈫�? What are (e) the magnitude and (f) the angle of a鈫�+b鈫�;(g) the magnitude and (h) the angle of b鈫�-a鈫�; and (i) the magnitude and (j) the angle ofrole="math" localid="1656943686601" a鈫�-b鈫�? (k) What is the angle between the directions of b鈫�-a鈫�anda鈫�-b鈫�?

Two vectors a鈫�and b鈫�have the components, in meters ax=3.2,role="math" localid="1657003775216" ay=1.6,bx=0.50,by=4.5,(a) Find the angle between the directions of a鈫�and b鈫�.There are two vectors in the xy plane that are perpendicular to a鈫�and have a magnitude of 5.0 m. One, vector c鈫�, has a positive x component and the other, vector d鈫�, a negative x component. What are (b) the x component and (c) the y component of vector, and (d) the x component and (e) the y component of vectord鈫�?

Being part of the 鈥淕ators,鈥� the University of Florida golfing team must play on a putting green with an alligator pit. Figure 3-22 shows an overhead view of one putting challenge of the team; an xy coordinate system is superimposed. Team members must putt from the origin to the hole, which is at xy coordinates (8 m, 12 m), but they can putt the golf ball using only one or more of the following displacements, one or more times:d1鈬赌=(8m)i^+(6m)j^,d2鈬赌=(6m)j^,d3鈬赌=(8m)i^The pit is at coordinates (8 m, 6 m). If a team member putts the ball into or through the pit, the member is automatically transferred to Florida State University, the arch rival. What sequence of displacements should a team member use to avoid the pit and the school transfer?
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