Question

The minute hand of a clock is 4 cm long. Find the average velocity of the tip of the minute
hand between 11:00 am to 11:30 am and between 11:00 am to 11:30 pm.
​

Answer 1

Answer:

Average velocity is π / 750 m/s

Explanation:

Data:

Radius = r = length of minutes hand = 4 cm = 0.04 m

First time = t1 =11 : 30 am - 11 : 00 am = 30 mint = 30 × 60 = 1800 sec

Second time = t2 = 11 : 30 pm - 11 : 00 am = 12 : 30 = (12 × 60 + 30) mint

                             = 720 + 30 = 750 minutes = 750 × 60 sec = 45000 sec

Required:

Average velocity = V = ?

Calculation:

We first find the velocity V1 when time is t1

Distance covered by hand in mint = circumference = 2πr = 2π(0.04)

                                                         =  0.08π m

Distance covered by hand in 30 mint = D1 = 30(0.08π) m = 2.4π m

we know that

velocity = distance / time

So

V1 = D1 / t1 = 2.4π / 1800 m/s

Similarly

For velocity V2 when time is t2

Distance covered in time t2 = 0.08π × 750 = 60π m

V2 = D2 / t2 = 60π / 45000 m/s

NOW

we know that

Average velocity = V = ( V1 + V2 ) / 2

Putting values we get

V = { ( 2.4π / 1800 ) +  ( 60π / 45000 ) } / 2 = π / 750 m/s

So

Average velocity is π / 750 m/s

Answer 2

Answer:

Hope this helped you.

Thank you.