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find the ratio of average speed and magnitude of average velocity of tip of a minute hand in 20 minutes
Average speed = distance / time

distance travelled by minute hand in 20 s = (1/3) (2πR )

where R is length of minute hand.

Average speed = [ (1/3) (2πR )] / ( 20 × 60 ) = ( π / 1800 ) R  m/s

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Average velocity = displacement / time

Since the motion is on a plane , Average velocity has two components

Average x-velocity  vx = x-displacement / time

( Polar coordinates are used to get displacements )

Average x-velocity vx  = [ R cos330 - R cos90 ] / (20×60) = ( √3 / 2400 ) R   m/s

Average y-velocity vy = y-displacement / time

Average y-velocity vy = [ R sin330 - R sin90 ] / (20×60) = ( -3 / 2400 ) R   m/s

magnitude of Average velocity  v =   m/s
Ratio of average speed to magnitude of average velocity is determined as follows

Answered by Thiyagarajan K | 18 Jul, 2022, 01:31: PM

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