[Math] Relative speed of minute hand in a clock

arithmeticgeometryrecreational-mathematics

In a 12 hours clock:

The minute hand has to chase the hour hand with a relative speed of 5.5 degrees/min

what is the mathematical derivation of this relative speed?

Best Answer

The hour hand rotates at $0.5$ degrees per minute and the minute hand rotates at $6$ degrees per minute...

Related Solutions

[Math] Deriving, diff b/w angles of minute and hour hands =11m/2-30h

As the hour hand, in $1$ minutes rotates $\displaystyle\frac12^\circ,$

So, in $h$ hour $m$ minute $\displaystyle =60h+m$ minute it will rotate $\displaystyle \left(\frac{60h+m}2\right)^\circ=\left(30h+\frac m2\right)^\circ$

Similarly, in $h$ hour $m$ minute the minute hand will rotate $\displaystyle 6(60h+m)^\circ\equiv 6m^\circ\pmod{360^\circ}$ assuming $h$ to be some integer

Now find the difference

[Math] The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much a day does the clock gain

On a normal clock, the hand cross each other 11 times in 12 hours, which means that they cross once every $\dfrac{12}{11} = 1.090909…$ hours or every 1 hour, 5 minutes, and 27.272727… seconds. The incorrect clock gains about 27 seconds at every crossing, so each day it gains $22(27.272727… seconds)= 10 minutes every day.

Note: These answers are all similar enough that different methods of calculating the answer could be the reason for the varying results.

Best Answer

Related Solutions

[Math] Deriving, diff b/w angles of minute and hour hands =11m/2-30h

[Math] The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much a day does the clock gain

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