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The length of the minute hand is 200% of the length of the hour hand.In 1 hour, how much farther does the tip of the minute hand move than the tip of the hour hand? Round your answer to the nearest hundredth |
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Answer» Step-by-step explanation: since lengh of MINUTE hand is 200% of hour hand therefore ratios of LENGTH between. hour hand and minute hand= 1 : 2 lengh of hh= 20mm length of mh= 40 mm distance covered by hour hand in 1 hour (since time TAKEN to complete one round by hour hand is 12 HOURS.) = 2×pi× length/ time taken for complete 1 round = 2× 20×pi/12=10pi/ 3 ( say it is X)
X=. 10pi/3....................(1) similarly if length of minute hand be 2 unit then distance covered by it in 1 hour (since time taken to complete one round by minute hand= 1 hour) = 2×pi×40/ 1 = 80pi unit ( say it is Y) Y = 80pi ......................(2) Therefore difference of distances covered by these two hands = ( 80pi -10 pi/3) =. (22/7)(80-10/3) = 22×230/21 = 240.95 mm since minute hand is 20 minute before than the hour hand according as the figure given. => difference between these two hands. = 1- 20/60 of 240.95 2/3 of 240.95 = 160.63 mm hence tip of minute hand will be 160.63 mm ahead from hour hand after one hour. |
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