Question

If the ratio of distances travelled by freely falling body in the last and last but one second of its motion is $7:5$. The velocity with which the body strikes the ground is : (Given $g=9.8m{s}^{-2}$)

• A. $29.4m{s}^{-1}$
• B. $39.2m{s}^{-1}$
• C. $19.6m{s}^{-1}$
• D. $49m{s}^{-1}$

Answer 1

Answer: (B)

$39.2m{s}^{-1}$

$\frac{s_n-s_{n-1}}{s_{n-1}-s_{n-2}}=\frac{7}{5}$

$\Rightarrow \frac{\left[u\right(n)+\frac{1}{2}g{n}^2]-\left[u\right(n-1)+\frac{1}{2}g(n-1{)}^2]}{\left[u\right(n-1)+\frac{1}{2}g(n-1{)}^2]-[u(n-2)+\frac{1}{2}g(n-2{)}^2]}=\frac{7}{5}$

$\Rightarrow \frac{u+\frac{1}{2}g(2n-1)}{u+\frac{1}{2}g(2n-3)}=\frac{7}{5}$

$u=0$ as body is freely falling

$\frac{2n-1}{2n-3}=\frac{7}{5}\Rightarrow n=4$

$v=gt\to$ at bottom most pt

$v=g\left(4\right)=9.8\times 4=39.2m/s$