Question

A body released from the top of a tower falls through half the height of the tower in $2$ s. In what time shall the body fall through the height of the tower?

• A. $4s$
• B. $3.26s$
• C. $3.48s$
• D. $2.828s$

Answer 1

The correct option is D $2.828s$

$h=ut+0.5a{t}^2$
For constant acceleration $\left(a\right)$ and zero initial velocity$\left(u\right)$
$h\propto t^2\Rightarrow \frac{h_1}{h_2}=\frac{t_1^2}{t_2^2}\Rightarrow t_2=\sqrt{\frac{h_2}{h_1}}\times t_1=\sqrt{2}\times t_1=\sqrt{2}\times 2s=2.828s$