Question

A body dropped from top of a tower fall through $60m$ during the last $2s$ of its fall. The height of tower is (take, $g=10m/s^2$)

• A. $95m$
• B. $60m$
• C. $80m$
• D. $90m$

Answer 1

The correct option is C

$80m$

Step 1. Given data:

Distance covered in last $2secondsish’=60m$

Let assume the total time of free fall is $Tseconds$,

And total distance covered is $h$.

Step 2. Calculating total time $\mathit{T}$ of the free fall:

From $2^{nd}$equation of motion, Total distance $h$ covered in free fall is

$h=ut+\frac{1}{2}a{t}^2$ $\left[u=0,t=Tandg=10m/s^2\right]$

$\Rightarrow h=0+\frac{1}{2}\times 10\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.\times T^2$

$\Rightarrow h=5T^2$ ____$\left(1\right)$

Distance covered by body in last $2s$ is

$$\begin{gathered} h’=g(T-2)x2+\frac{1}{2}g{\left(2\right)}^2 \\ \Rightarrow 60=(20(T-2)+20) \\ \Rightarrow T=4s \end{gathered}$$

Putting value of $\mathit{T}$ in equation $\left(1\right)$

$$\begin{gathered} h=5T^2 \\ \Rightarrow h=5\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.\times 4^2{\mathrm{s}}^2 \\ \Rightarrow h=80m \end{gathered}$$

Hence, option C is correct.