First slide

Rectilinear Motion

Question

A ball is thrown straight upward with a velocity v₀ from a height h above the ground. The time taken for the ball to strike the ground is

Moderate

A

$\frac{v_{0}}{g} (1 + \frac{2 g h}{v_{0}^{2}})$
B

$\frac{v_{0}}{g} (\sqrt{1 + \frac{2 g h}{v_{0}^{2}}})$
C

$\frac{v_{0}}{g} (1 - \sqrt{1 + \frac{2 g h}{v_{0}^{2}}})$
D

$\frac{v_{0}}{g} (1 + \sqrt{1 + \frac{2 g h}{v_{0}^{2}}})$

Solution

$\begin{array}{l} Apply s = u t + \frac{1}{2} a t^{2} \\ \Rightarrow - h = v_{0} t - \frac{1}{2} g t^{2} \Rightarrow g t^{2} - 2 v_{0} t - 2 h = 0 \\ \Rightarrow t = \frac{2 v_{0} \pm \sqrt{4 v_{0}^{2} + 8 g h}}{2 g} \end{array}$
As t is not negative, so ignoring negative sign, we get
$t = \frac{2 v_{0} + 2 \sqrt{v_{0}^{2} + 2 g h}}{2 g} = \frac{v_{0}}{g} [1 + \sqrt{1 + \frac{2 g h}{v_{0}^{2}}}]$

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