Question

A ball is dropped from a bridge of 122.5 metre above a river. After the ball has been falling for two seconds, a second ball is thrown straight down after it. Initial velocity of second ball so that both hit the water at the same time is

• A. $49m/s$
• B. $55.5m/s$
• C. $26.1m/s$
• D. $9.8m/s$

Answer 1

The correct option is C $26.1m/s$

For the first ball$:$ Let it takes ${}^{\prime }{t}^{\prime }sec$ to river$.$

$\Rightarrow 122.5=\frac{1}{2}\times g\times t^2$------------------------$\left(1\right)$$

for second ball$:$ time taken $=t-2sec.$

$122.5=u\left(t-2\right)+\frac{1}{2}g{\left(t-2\right)}^2$--------------$\left(2\right)$

$\Rightarrow \frac{g{t}^2}{2}=ut-2u+\frac{g{t}^2}{2}+2g-2gt$

$\Rightarrow \left(2g-u\right)t=2g-2u$

$\Rightarrow t=\frac{2g-2u}{2g-u}$

from$\left(1\right)$

$t^2=\frac{2\times 122.5}{g}$

$t=\sqrt{\frac{2\times 122.5}{98}}=\frac{35}{7}=5\sec$

$\Rightarrow 10g-5u=2g-2u$

$\Rightarrow 8g=3u$

$u=\frac{8\times 9.8}{3}=26.1m/s$

Hence,

option $\left(C\right)$ is correct answer.