Question

a stone is dropped from top of a tower covers 11/36th of total height in the last second of its journey. calculate the height of the tower??

Answer 1

Answer:

~Hey mate...

Here's ur answer :

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Let,

the height of the tower is H meter & the time taken to fall H meter is t sec.

»» By, s = ut + 1/2gt^2

»» H = 0 + 1/2(10)t^2

»» H = 5t^2 ......(1)

Now,

the distance it fall in (t-1) sec

»» By, s = ut + 1/2gt^2

»» s = 0 + 1/2(10)t^2

»» s = 5t^2 ......(2)

By, Eqn (1) - (2) :-

»» the distance covered in last sec = H-s

»» 11H/36 = 1/2g[t^2 - (t-1)^2]

»» 11H/36 = 1/2(10)(2t-1)

»» 11H/36 = 5(2t-1) ......(3)

by eqn (1) & (3),

» 11/36 * 5t^2 = 5(2t-1)

» 11t^2 = 72 - 36

» 11t^2 - 72 + 36 = 0

» t = [-(-72) ± √{(-72)^2 - 4*11*36}]/[2*11]

» t = [-(-72) ± 60]/22

» t = 6 sec OR 0.55 sec

Thus, By eqn (1),

»» H = 5t^2

.°. »» H = 180 m OR 1.51 m

But, H ≠ 1.51 m (since, Height is maximum)

Hence, H = 180 m ,,

Therefore, the total height of the tower is 180 m.

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✨❤Hope it helps❤✨