Calculate how many times the speed of the end of the minute hand is greater than the speed

| April 12, 2021 | education

Calculate how many times the speed of the end of the minute hand is greater than the speed of the end of the hour hand if the minute hand is 1.5 times longer than the hour hand.

Let the length of the hour hand be R. Then, according to the problem statement, the length of the minute hand is 1.5 * R.

The length of the circle that the end of the hour hand describes is L1 = 2 * pi * R, then the speed of the hour hand is v1 = L1 / 60 minutes = 2 * pi * R / 60 m / minute.

The length of the circle that the end of the minute hand describes is L1 = 2 * pi * 1.5 * R, then the speed of the hour hand is v2 = L1 / 1 minute = 2 * pi * 1.5 * R / 1 = 3 * pi * R.

The ratio of the speeds of the minute and hour hands will be equal to:

v2 / v1 = 3 * pi * R / (2 * pi * R / 60) = 3 * pi * R * 60/2 * pi * R = 3 * 60/2 = 180/2 = 90.

Answer: The speed of the minute hand is 90 times the speed of the hour hand.



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