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Finding Average Velocity

A bullet is f...

Question

A bullet is fired vertically up from a $400 m$ tall tower with a speed of $80 m / s$ . If $g$ is taken as $10 m / s^{2}$ ,then the time taken by the bullet to reach the ground will be

8 s

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16 s

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20.35 s

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22.65 s

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Solution

The correct option is C $22.65 s$
Taking upward direction as $p o s i t i v e$ we will get the $d o w n w a r d$ displacement as $- 400 m e t e r$
so putting $s = - 400 m$ , $u = 80 m / s$ , $a = - g = - 10 m / s^{2}$
and using $s = u t + \frac{1}{2} a t^{2}$
we get $- 400 = 80 t - 5 t^{2}$
on solving ( Just employ the Shridharacharya Formula $t = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
Where $t$ is root of $a t^{2} + b t + c = 0$ )
we get $t = 22.65 s$

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