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Chapter 3: Q23P (page 58)

If is B⇀added to C⇀=3.0i+4.0j^, the result is a vector in the positive

direction of the y axis, with a magnitude equal to that of C⇀. What is the

magnitude ofB⇀?

Short Answer

Expert verified

Magnitude of B⇀=3.2

Step by step solution

01

To understand the concept

The resultant in this problem is in the positive y-direction so the x component will be zero and having magnitude equal to C. The magnitude of the unknown vector can be calculated using the law of addition which is explained by the following equation.

A⇀=xi^+yj^

Thus the magnitude is given by

A⇀=x2+y2

Given are

B⇀+C⇀=R⇀

Where R⇀is the resultant

C⇀=3i^+4j^C=R

02

To find magnitude of vector C⇀

C⇀=3i^+4j^

Using the equation (ii), magnitude of the vector C⇀can be written as

C⇀=32+42C⇀=5

03

To find magnitude of vector B⇀

As the resultant in the positive y direction

R⇀=5j^B⇀+C⇀=R⇀B⇀+3i^+4j⇀=5j⇀B⇀=-3i^+j^B⇀=-32+12B⇀=3.2

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Most popular questions from this chapter

A cat rides a merry-go-round turning with uniform circular motion. At time t1=2.00s, the cat’s velocity is v⇀1=(3.00m/s)i^+(4.00m/s)j^, measured on a horizontal xy coordinate system. Att2=5.00s , the cat’s velocity is v⇀2=(-3.00m/s)i^+(-4.00m/s)j^.What are (a) the magnitude of the cat’s centripetal acceleration and (b) the cat’s average acceleration during the time intervalt2-ti, which is less than one period?

A car is driven east for a distance of 50 km, then north for 30 km, and then in a direction 30°east of north for 25 km . Sketch the vector diagram and determine (a) the magnitude and (b) the angle of the car’s total displacement from its starting point.

Vector d→1is in the negative direction of a y axis, and vector d2→is in the positive direction of an x axis. What are the directions of (a) d2→/4and (b) d1/(-4)? What are the magnitudes of products (c) d→1-d→2and (d) d→1.(d→2/4)? What is the direction of the vector resulting from (e) d→1×d→2and (f)d→1×d→2? What is the magnitude of the vector product in (g) part (e) and (h) part (f)? What are the (i) magnitude and (j) direction ofd→1×(d→2/4)?

Describe two vectorsa⇀andb⇀such that

a)a⇀+b⇀=c⇀anda+b=c;b)a⇀+b⇀=a⇀-b⇀;c)a⇀+b⇀=c⇀anda2+b2=c2

A room has dimensions 3.00m(height)×3.70×4.30m. A fly starting at one corner flies around, ending up at the diagonally opposite corner. (a) What is the magnitude of its displacement? (b) Could the length of its path be less than this magnitude? (c) Greater? (d) Equal? (e) Choose a suitable coordinate system and express the components of the displacement vector in that system in unit-vector notation. (f) If the fly walks, what is the length of the shortest path? (Hint: This can be answered without calculus. The room is like a box. Unfold its walls to flatten them into a plane.)
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