The minute hand of a clock is 14m long. the approximate distance covered and displacement of the tip of the minute hand during the interval the time changes from 5:05 to 7:20 pm are =
Step 1: Given that:
The length of the minute hand of the clock= 14m
Given time interval= 5:05pm−7:20pm = 2hr15minutes
Step 2: The distance covered by the minute hand of the clock in given time:
Now,
The distance covered by the minute hand in two complete rounds is given by;
d=2× Circumference of the circular path covered by minute hand with its length as the radius of the path.
Thus,
d=2×2πr , where r is the length of the minute hand of the clock
d=2×2×227×14m
d=4×22×2
d=196m
The distance covered by the minute hand in the next 15 minutes will be
d′=14× the circumference covered by the minute hand with its length as the radius
d′=14×2×227×14m
d′=11×2
d′=22m
Thus,
The total distance covered by the minute hand in the given time will be
D=d+d′
D=196m+22m
D=218m
Step 3: Calculation of displacement of the tip of the minute hand in the given time:
In one complete round,
Displacement of minute hand= 0
Thus, the displacement of the tip of the minute hand in 2hrs that is in two complete rounds will be 0.
In the next 15minutes displacement will be:
Thus, the displacement will be calculated by using the Pythagoreus theorem
Displacement= √(142+142)
= 14√2m
Thus total displacement in the given time will be, 14√2m .
Hence,
In given time,
Total distance covered by minute hand= 218m
Total displacement covered = 14√2m