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.

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