Half Time At 3:00 the hour hand and the minute hand of a clock point in directions that are 90.0 apart. What is the first time after 3

Question

Half Time At 3:00 the hour hand and the minute hand of a clock point in directions that are 90.0
apart. What is the first time after 3:00 that the angle between the two hands has decreased by half to 45.0?

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Hưng Khoa 4 years 2021-08-31T12:32:06+00:00 1 Answers 60 views 0

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  1. thuhuong
    0
    2021-08-31T12:33:58+00:00
    Reply

    Answer:

    3 : 08 : 10.9

    Explanation:

    assuming a 12 hour clock

    angular velocity of the hour hand is 2π/(3600(12)) rad/s

    angular velocity of the minute hand is 2π/3600 rad/s

    difference is 2π/3600 – 2π/(3600(12)) = 11(2π/(3600(12)) rad/s

    45° = π/4 radians

    This angle is covered in a time of

    π/4 rad / 22π / (3600(12)) = 900(12) / 22 = 490.909090… s

    or about 8 minutes 10.9 s

    ANSWER 3:08:10.9

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