Question

A particle is projected upwards from top of a tower of height $40m$ with a speed of $10m/s$. The time it will take to strike ground $(g=10m/s^2)$ will be

• A. $1s$
• B. $2s$
• C. $3s$
• D. $4s$

Answer 1

The correct option is D $4s$

The time taken to strike the ground would be found by taking the downward direction to be $+ve$
So initial velocity $u=-10m{s}^{-1},s=40m$
And $a=g=10m{s}^{-2}$
To find the time we will use $s=ut+\frac{1}{2}a{t}^2$
$\Rightarrow 40=-10t+\frac{1}{2}\times 10\times t^2$
$\Rightarrow t^2-2t-8=0$
$\Rightarrow t^2-4t+2t-8=0$
$\therefore (t-4)(t+2)=0$ and as time cannot be negative so $t=-2$ is rejected.
$\therefore t=4s$ is the correct answer.