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Chapter 3: Q78P (page 61)

What is the magnitude a鈫�脳(b鈫�脳a)鈫�of if a = 3.90 , b = 2.70and the angle between the two vectors is localid="1656307928946" 63.0掳?

Short Answer

Expert verified

The magnitude is36.6

Step by step solution

01

To understand the concept

This problem is based on the vector product. When two vectors are multiplied by the sine of the angle between them, the magnitude of the vector product can be found.

The vector product of two vectors a鈫�and b鈫�is given by

c鈫�=(b鈫�脳a鈫�) (1)

And the magnitude is given by

c=ab蝉颈苍胃(2)Givena=3.90b=2.70Anglebetweenthesetwovectorsis胃=36.6

02

To find the magnitude ofa→×(b→×a)→

Here, vector is perpendicular to vectora鈫�Thus the magnitude of role="math" localid="1656307375446" (a鈫�脳c鈫�)is given by,

acsin(90)=ac

Using equation (i) and (ii), the magnitude of a鈫�脳(b鈫�脳a鈫�)is

a鈫�脳(b鈫�脳a)鈫�=ac=a2b蝉颈苍胃 (3)

Substituting the given values of a and b in equation (iii),

a鈫�脳(b鈫�脳a)鈫�=(3.90)2(2.70)sin(63)=36.6

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Most popular questions from this chapter

Oasis Bis 25kmdue east of oasis A, a camel walks 24kmin a directionlocalid="1656942587340" 15掳south of east and then walks 8.0kmdue north. How far is the camel from oasis B?

A鈫�has the magnitude12.0mand is angled60掳counterclockwise from the positive direction of the x axis of anxy coordinate system. Also,B鈫�=(12.0m)i^+(8.0m)j^on that same coordinate system. We now rotate the system counter clockwise about the origin by20掳 to form anx'y' system. On this new system, what are (a)A鈫�and (b)B鈫�, both in unit-vector notation?

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

Here are three displacements, each measured in meters: d鈫�1=4.0i铃�+5.0j铃�-6.0k铃�,d鈫�2=-1.0i铃�+2.0j铃�+3.0k铃�,andd鈫�3=4.0i铃�+3.0j铃�+2.0k铃�. (a) What is r鈫�=d鈫�1+d鈫�2+d鈫�3? (b) What is the angle betweenr鈫�and the positive z axis? (c) What is the component of d1along the direction of d鈫�2(d) What is the component of d鈫�1that is perpendicular to the direction of d2鈫�and in the plane of role="math" localid="1658465314757" d鈫�1and d鈫�2(Hint: For (c), consider Eq 3-20.and Fig, 3-18; for (d), consider Eq.3-24.)

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 鈥渇orward鈥�) of the knight鈥檚 overall displacement for the series of three moves?
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