Question

A ball is projected horizontally from top of a $80\text{m}$ deep well with velocity $10\text{m/s}$. Then the ball will fall to the bottom at a distance of (the speed of the ball does not change in any collision)

• A. $5\text{m}$ from $A$
• B. $5\text{m}$ from $B$
• C. $2\text{m}$ from $A$
• D. $2\text{m}$ from $B$

Answer 1

Answer: (B), (C)

The correct options are
B $5\text{m}$ from $B$
C $2\text{m}$ from $A$

Horizontal distance travelled in between 2 successive collisions $=7\text{m}$

Let time taken in one collision is $t$
Then $t\times 10=7\Rightarrow t=0.7\text{sec}$.
Total time taken by the ball to reach at bottom $=\sqrt{\frac{2H}{g}}=\sqrt{\frac{2\times 80}{10}}=4\text{sec}$.
No. of collisions $=\frac{4}{0.7}=\frac{40}{7}=5\frac{5}{7}$ ($5th$ collision from wall $B$)

$\therefore$ Horizontal distance travelled in $\frac{5}{7}th$ part of collision $=\frac{5}{7}\times 7=5\text{m}$, so distance from $B$ is $5\text{m}$ and distance from $A$ is $2\text{m}$.