Question

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

• A. 1 s
• B. 2 s
• C. 3 s
• D. 4 s

Answer 1

The correct option is D 4 s

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 $s=ut+\frac{1}{2}a{t}^2$
$\Rightarrow 40=-10t+\frac{1}{2}\times 10\times t^2$
$\Rightarrow t^2–2t–8=0$
$\Rightarrow t^2–4t+2t–8=0$
$\therefore (t-4)(t+2)=0$
As time cannot be negative so $t=-2$ is rejected
$\therefore t=4s$ is the correct answer.