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Grade 12th passMechanics

A particle is dropped from top of tower. If it falls half of the height of the tower in its last second of journey. Find the time of journey.

Profile image of Karthik
7 Years agoGrade 12th pass
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1 Answer

Profile image of Arun
7 Years ago

h = ut +0.5 gt2

as u =0 and g =10 m/s2

Let total height = H

Total time = T

H = 0 5 gT2 = 5 T2

Distance travelled in nth second ( last second )

Sn = 0.5 g ( n2 — ( n-1)2 ) = 0.5 g ( 2n-1) = H/2

So 0.5 gT2 /2 = 0.5 g ( 2n -1) = 5 (2n -1 )

H/2 = 5 (2n-1)

Put the value of H equal to 5 T2 and n = T

T2 /2 = ( 2T-1)

T2 = 2 ( 2T-1)

T2 = 4T -2

T2 -4T +2 = 0

Using quadratic solutions

T can be 3.415 Or 0.585

Now 0.585 is not possible

So T = 3.415 second