A ball is dropped from top of a tower of 1

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A ball is dropped from top of a tower of $100\,m$ height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of $50\, m/s$ ($g = 10\,m/{s^2})$. They will cross each other after..........$s$

A

$1$

B

$2$

C

$3$

D

$4$

A ball is dropped from top of a tower of $100\,m$ height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of $50\, m/s$ ($g = 10\,m/{s^2})$. They will cross each other after..........$s$

${h_1} = \frac{1}{2}g{t^2}$, ${h_2} = 50t - \frac{1}{2}g{t^2}$

Given ${h_1} + {h_2} = 100\,m$

$⇒$ $50t = 100 \Rightarrow t = 2\;\sec $