Question

A body dropped from the top of a tower covers the distance $7x$ in the last second of its journey, where $x$ is the distance covered in $1\text{st}$ sec. How much time does it take to reach the ground ?

• A. $3\text{sec}$
• B. $4\text{sec}$
• C. $5\text{sec}$
• D. $6\text{sec}$

Answer 1

The correct option is B $4\text{sec}$

Let's say it takes $n$ sec to reach the ground.

Since it is dropped so $u=0$

Distance covered in $1^{st}$ second is $x$.

Using kinematics relation

$s=ut+\frac{1}{2}g{t}^2$

Putting the value of given parameters

$\Rightarrow x=0+\frac{1}{2}g{\left(1\right)}^2=\frac{g}{2}........\left(1\right)$

Similarly, distance in $n^{th}$ (last) second is

$7x=u+\frac{1}{2}g(2n-1)$

$\Rightarrow 7x=\frac{1}{2}g(2n-1)....\left(2\right)$

From Eqs. $\left(1\right)$ and $\left(2\right)$,

$\Rightarrow 7=2n-1$

$\Rightarrow n=4\text{seconds}$

Hence, option $\left(b\right)$ is the correct answer.