Question

A bullet fired vertically up from the ground reaches a height 40 m in its path from the ground and it takes further time 2 seconds to reach the same height.$\left(g=10m{s}^{-2}\right)$ The total time of flights is

• A. 4s
• B. 3s
• C. 6s
• D. 8s

Answer 1

The correct option is C 6s

$\left(D\right)$

using : $s=ut-\frac{g{t}^2}{2}$
simplyfing : $g{t}^2-2ut+2h=0$

For a given value of h the above equation gives two solution $t_1\&t_2$

$t_2-t_1=\frac{2\sqrt{u^2-2gh}}{g}$

$2=\frac{2\sqrt{u^2-2gh}}{g}$

$u^2=2gh+g^2$

$\frac{u}{g}=\sqrt{1+\frac{2h}{g}}$

$T=\frac{2u}{g}=2\sqrt{1+\frac{2h}{g}}=6sec$