A ball is shot vertically upward with a given initial velocity. It reaches a maximum height of $100\text{m}$. If in the second shot the initial velocity is doubled then the ball will reach a maximum height of

The correct option is D $400\text{m}$
Let the initial velocity at the first shot be $u$, then from third equation of motion
$v^2=u^2+2aS$
$O=u^2–2g\left(100\right)$
$u^2=2g\left(100\right)$
Now, for the second shot similarly
$(2u{)}^2=2g(H)$
$4u^2=2gH$
$4\left(2g\right(100\left)\right)=2gH$
$H=400\text{m}$
Therefore, option D is correct.