Question

Find the initial velocity of projection of a ball thrown vertically up if the distance moved by it in 3rd second is twice the distance covered by it in 5th second.$(Takeg=10{ms}^2)$

• A. $45{ms}^{-1}$
• B. $75{ms}^{-1}$
• C. $20{ms}^{-1}$
• D. $85{ms}^{-1}$

Answer 1

The correct option is B $75{ms}^{-1}$

Let initial velocity $u$,

Let $S_1$ be the distance covered in $n$ seconds and $S_2$ be the distance covered in $(n+1)$.

Let $S_n$ be the distance covered in $nth$ seconds.

Using $s=ut+\frac{1}{2}a{t}^2$, $\Rightarrow S_1=un-\frac{1}{2}g{n}^2$ ....1

$\Rightarrow S_2=u(n+1)-\frac{1}{2}g(n+1{)}^2$ ....2

Subtracting equations 1 from 2, $S_2-S_1=u(n+1)-\frac{1}{2}g{n}^2-(un-\frac{1}{2}g(n+1{)}^2)$

$\Rightarrow S_n=S_2-S_1=u-\frac{1}{2}(2n+1)$

$\therefore S_3=u-35$ ......3

$\therefore S_5=u-55$ ......4

Using the condition given in question , $S_3=2S_5$

$\Rightarrow u-35=2(u-55)$ $\Rightarrow u=75m{s}^{-1}$