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Chapter 3: Q4P (page 57)

Express the following angles in radians: (a)20.0掳,(b)50.0掳,100掳Convert the following angles to degrees:(d)0.330rad,(e)2.10rad,(f)7.70rad

Short Answer

Expert verified

a)Anglesinradians;20.0掳=0.349rad50.0掳=0.873rad100.0掳=1.75radb) Anglesindegrees:0.330rad=18.9掳0.330rad=120掳0.330rad=441掳

Step by step solution

01

Understanding the relation between degree and radian.

360掳of2蟺radof makes up a complete circle angle. This means a circle subtends an angle with radian 2蟺and degree 360掳 at its centre. An angle's measure can be converted from one unit to another based on the following formula.

360掳=2蟺rad(1)Givenaretheanglesindegrees20掳,50掳,100掳andAnglesinradians0.330rad.2.10rad,7.70rad.

02

To calculate angle in radians part a)

Using equation (i) the angle can be expressed in radians as

20.0掳=((20.0掳)2蟺360掳rad=0.349rad50.0掳=((50.0掳)2蟺360掳rad=0.873rad100.0掳=((100.0掳)2蟺360掳rad=1.75rad

03

To calculate angle in degrees part b)

Using equation (i) the angle can be expressed in degrees as

0.330rad=(0.330rad)360掳2蟺rad=18.9掳2.10rad=(2.10rad)360掳2蟺rad=120掳7.70rad=(7.70rad)360掳2蟺rad=441掳

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Most popular questions from this chapter

Consider a鈫�in the positive direction of x, b鈫�in the positive direction of y, and a scalar d. What is the direction of b鈫�/dif d is

(a) positive and

(b) negative? What is the magnitude of

(c)a鈫�鈰�b鈫�and (d)a鈫�鈰�b鈫�/d?

What is the direction of the vector resulting from (e)a鈫�脳b鈫�and (f)b鈫�脳a鈫�?

(g) What is the magnitude of the vector product in (e)?

(h) What is the magnitude of the vector product in (f)? What are

(i) the magnitude and

(j) the direction of a鈫�脳b鈫�/dif d is positive?

In Fig. 3-38 , the magnitude of a鈬赌is4.3, the magnitude of b鈬赌is5.4, and 蠒=46掳. Find the area of the triangle contained between the two vectors and the thin diagonal line.

In a meeting of mimes, mime 1 goes through a displacementd鈫�1=(4.00m)i铃�+(5.00m)j铃�and mime 2 goes through a displacementd鈫�2=(-3.0m)i铃�+(4.0m)j铃�. What are (a) d鈫�1脳d鈫�2, (b) d鈫�1.d鈫�2, (c) (d鈫�1+d鈫�2)d鈫�2, and (d) the component ofd鈫�1along the direction ofd鈫�2? (Hint: For (d), see Eq.3-20and fig3-18.)

A particle undergoes three successive displacements in a plane, as follows:d1鈫�, 4.00 m southwest; then d2鈫�, 5.00 m east; and finally d3鈫�, 6.00 m in a direction 60掳north of east. Choose a coordinate system with the y axis pointing north and the x axis pointing east. What are (a) the x component and (b) the y component of d1鈫�? What are (c) the x component and (d) the y component of d2鈫�? What are (e) the component and (f) the y component of d3鈫�? Next, consider the net displacement of the particle for the three successive displacements. What are (g) the x component, (h) the y component, (i) the magnitude, and ( j) the direction of the net displacement? If the particle is to return directly to the starting point, (k) how far and (l) in what direction should it move?

For the following three vectors, what is 3C鈫�.(2A鈫�脳B鈫�)?

A鈫�=2.00i^+3.00j^-4.00k^,B鈫�=-3.00i^+4.00j^+2.00k^,C鈫�=7.00i^-8.00j^
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