u s r 6 30 1 rad 5 11.46 in VS .NET

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u s r 6 30 1 rad 5 11.46
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1.5 A railroad curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25 in a distance of 120 m
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We are finding the radius of a circle on which a central angle 120 m. Then r s u 12 5p>36 864 p m 275 m 25 5 /36 rad intercepts an arc of
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1.6 A train is moving at the rate of 8 mi/h along a piece of circular track of radius 2500 ft. Through what angle does it turn in 1 min
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Since 8 mi/h 8(5280)/60 ft/min 704 ft/min, the train passes over an arc of length s 1 min. Then s/r 704/2500 0.2816 rad or 16.13 . 704 ft in
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1.7 Assuming the earth to be a sphere of radius 3960 mi, find the distance of a point 36 N latitude from the equator.
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Since 36 /5 rad, s r 3960( /5) 2488 mi.
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1.8 Two cities 270 mi apart lie on the same meridian. Find their difference in latitude.
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u s r 270 3960 3 rad 44 or 3 54.4r
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1.9 A sector of a circle has a central angle of 50 and an area of 605 cm2. Find the radius of the circle. K 1r2u; therefore r 22K/u. 2
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r 2K Bu 37.2 cm 2(605) B (5p>18) 4356 B p 21386.56
1.10 A sector of a circle has a central angle of 80 and a radius of 5 m. What is the area of the sector
1 2 2r u
4p 1 2 2 (5) a 9 b
50p 2 m 9
17.5 m2
1.11 A wheel is turning at the rate of 48 r/min. Express this angular speed in (a) r/s, (b) rad/min, and (c) rad/s.
(a) 48 (b) 48 r min 48 r # 1 min 1 min 60 s 48 r 1 min 48 r 1 min 4r 5s
r min r (c) 48 min
rad rad # 2p rad 96p or 301.6 1 r min min 8p rad rad # 1 min # 2p rad or 5.03 s 60 s 1 r 5 s
1.12 A wheel 4 ft in diameter is rotating at 80 r/min. Find the distance (in ft) traveled by a point on the rim in 1 s, that is, the linear velocity of the point (in ft/s).
80 r min 80a 2p rad b s 60 8p rad 3 s
CHAPTER 1 Angles and Applications
Then in 1 s the wheel turns through an angle 8 /3 rad and a point on the wheel will travel a distance r 2(8 /3) ft 16.8 ft. The linear velocity is 16.8 ft/s.
1.13 Find the diameter of a pulley which is driven at 360 r/min by a belt moving at 40 ft/s.
360 r min 360a 2p rad b s 60 rad 12p s 12 rad and a point on the rim travels a
Then in 1 s the pulley turns through an angle distance s 40 ft. d 2r s 2a b u 2a 40 bft 12p
20 ft 3p
2.12 ft
1.14 A point on the rim of a turbine wheel of diameter 10 ft moves with a linear speed of 45 ft/s. Find the rate at which the wheel turns (angular speed) in rad/s and in r/s.
In 1 s a point on the rim travels a distance s 45 ft. Then in 1 s the wheel turns through an angle 45/5 9 rad and its angular speed is 9 rad/s. Since 1 r 2 rad or 1 rad 1/2 r, 9 rad/s 9(1/2 ) r/s 1.43 r/s. s/r
1.15 Determine the speed of the earth (in mi/s) in its course around the sun. Assume the earth s orbit to be a circle of radius 93,000,000 mi and 1 year 365 days.
In 365 days the earth travels a distance of 2 r 2(3.14)(93,000,000) mi. 2(3.14)(93,000,000) In 1 s it will travel a distance s mi 18.5 mi. Its speed is 18.5 mi/s. 365(24)(60)(60)
SUPPLEMENTARY PROBLEMS
Use the directions for rounding stated on page 2.
1.16 Express each of the following in radian measure: (a) 25 , (b) 160 , (c) 75 30 , (d) 112 40 , (e) 12 12 20 , (f) 18.34 Ans. (a) 5 /36 or 0.4363 rad (b) 8 /9 or 2.7925 rad (c) 151 /360 or 1.3177 rad (d) 169 /270 or 1.9664 rad (e) 0.2130 rad (f) 0.3201 rad
Express each of the following in degree measure: (a) /4 rad, (b) 7 /10 rad, (c) 5 /6 rad, (d) 1/4 rad, (e) 7/5 rad Ans. (a) 45 , (b) 126 , (c) 150 , (d) 14 19 12 or 14.32 , (e) 80 12 26 or 80.21
On a circle of radius 24 in, find the length of arc subtended by a central angle of (a) 2/3 rad, (b) 3 /5 rad, (c) 75 , (d) 130 . Ans. (a) 16 in, (b) 14.4 or 45.2 in, (c) 10 or 31.4 in, (d) 52 /3 or 54.4 in
A circle has a radius of 30 in. How many radians are there in an angle at the center subtended by an arc of (a) 30 in, (b) 20 in, (c) 50 in Ans. (a) 1 rad, (b)
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