Question

A ball is thrown vertically upwards from the top of a tower of height $h$ with velocity $v$. The ball strikes the ground after

• A. $\frac{v}{g}\left[1+\sqrt{1+\frac{2 g h}{v^{2}}}\right]$
• B. $\frac{v}{g}\left[1+\sqrt{1-\frac{2 g h}{v^{2}}}\right]$
• C. $\frac{v}{g}\left(1+\frac{2 g h}{v^{2}}\right)^{1 / 2}$
• D. $\frac{v}{g}\left(1-\frac{2 g h}{v^{2}}\right)^{1 / 2}$

Answer 1

Answer: (A)

As, $h=-v t+\frac{1}{2} g t^{2}$
or $f t^{2}-2 v t-h=0$
$\Rightarrow t=\frac{-(-2 v) \pm \sqrt{4 v^{2}+4\, g h}}{2 g}=\frac{2 v \pm \sqrt{v^{2}+g h}}{2 g}$
$=\frac{v}{g} \pm \frac{\left[v^{2}+2\, g h\right]^{1 / 2}}{g}=\frac{v}{g}\left[1 \pm \sqrt{1+\frac{2\, g h}{v^{2}}}\right]$