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A body start from rest and fall vertically from a height of 19.6m. If g=9.8 then the time taken by the body to fall through the last m of its fall is

A body start from rest and fall vertically from a height of 19.6m. If g=9.8 then the time taken by the body to fall through the last m of its fall is 

Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
Initial velocity of the body = u = 0
Height through which the body has fallen = Distance traveled = s = 19.6 m
Time taken to fall through a distance s = t
Before the last meter of its fall, distance traveled = s' = 18.6 m
Time taken to fall through the distance s' = t'
Acceleration of the body = a = g = 9.8 m/s2
Applying the equation : s = ut + (1/2)at2 we have
19.6 = (1/2)(9.8)t2 ..... (1)
=> t2 = 2(19.6)/(9.8) = 4
=> t = 2 s 
18.6 = (1/2)(9.8)(t')2 ........ (2)
=>( t')2 = 2(18.6)/(9.8) = 3.796
=> t' = √(3.796) = 1.95 s
t - t' = 2 - 1.95 = 0.05 s
 
 
Regards
Arun

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