SOLUTION: Please help me with my homework.
1. A 40 cm pendulum swings through an angle of 15 degrees. Find the length of the arc through with the tip of a pendulum swings to the neares
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Question 145665: Please help me with my homework.
1. A 40 cm pendulum swings through an angle of 15 degrees. Find the length of the arc through with the tip of a pendulum swings to the nearest tenth of the centimeter.
2. Find the distance traveled by the tip of 7 cm min. hand of a clock in 7 and 1/2 min.
Thanks a lot! ! !
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. A 40 cm pendulum swings through an angle of 15 degrees. Find the length of the arc through with the tip of a pendulum swings to the nearest tenth of the centimeter.
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If the pendulum swung thru a 360 degree circle the circumference would
be 2(pi)40 = 80pi cm
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But it only swings thru 15 degrees of that circle.
So it's arc is (15/360)(80pi) = 3.3333..pi cm
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If you are supposed to arrive at an answer using radians
The arc length is r(theta) where theta is measured in radians:
For your problem theta 15(pi/180) radians,
so the arc length is (15)(pi/180)*40 = 3.3333... cm
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2. Find the distance traveled by the tip of 7 cm min. hand of a clock in 7 and 1/2 min.
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Find the angle associated with 7 1/2 min
(15/2/60)*360 = = (15/2)*6 = 45 degrees
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45 degrees = pi/4 radians
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arc length = r(theta) = 7(pi/4) = 5.4978... cm
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If you don't use the r(theta) formula you would get:
circumference = 14pi cm
then (45/360)*14pi = 1.75pi = 5.4978 cm
=======================
Cheers,
Stan H.
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