Clocks - Relative Velocity

Rarely Tested

CLOCKS:

  • The clock is a circle and there are 12 hour divisions in it. Total Angle=360°. Angle between 2 hours = 30°.
    The hour hand completes 30° in an hour i.e. 60 min. So, speed of hour hand=0.5°/min.
    The minute hand completes 360° in an hour i.e. 60 min. So, speed of minute hand=6°/min.  
    In a well functioning clock, both hands meet after every 720 / 11 Mins.
  • It is because the relative speed of the minute hand with respect to the hour hand = 11/2 degrees per minute.
  • Angle between hands at H hours M minutes = |30H - 11M/2| degrees
Question 1

What is the angle between the hour and minute hands of a clock 30 minutes after they meet for the third time in a day?

Question 2

At what time between 7:00 and 8:00 will the minute and hour hands of a clock be pointing at exactly opposite directions?

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