Question

A particle is dropped from the top of the tower of height $H$. Distance travelled by the particle in last second is $35\text{m}$. Find the height of the tower.
[Take $g=10{\text{m/s}}^2$]

• A. $35\text{m}$
• B. $45\text{m}$
• C. $80\text{m}$
• D. $60\text{m}$

Answer 1

The correct option is C $80\text{m}$

Given $u=0,s_{n^{th}}=35\text{m}$
As we know that the distance travelled by a particle in $n^{th}$ sec is given as
$S_{n^{th}}=u+\frac{a}{2}[2n-1]$
$\Rightarrow -35=0-\frac{g}{2}[2n-1]$
$\Rightarrow 70=10[2n-1]$
$\Rightarrow n=4\text{sec}$
So, the total time of flight is $n=t=4\text{sec}$
Thus, height of tower is given as
$-H=-\frac{1}{2}g{t}^2$
$\Rightarrow -H=-\frac{1}{2}\times 10\times 4^2$
$\Rightarrow H=80\text{m}$