Question

A body falling from height 'H' takes time 'T' seconds to reach the ground. The time taken to cover the second half of height is

• A. $\frac{T}{\sqrt{2}}$
• B. $\sqrt{2}T$
• C. $(\frac{\sqrt{2}-1}{\sqrt{2}})T$
• D. $(\frac{1}{\sqrt{2}-1})T$

Hint:

Time to fall the first half is roughly 70% ($1/\sqrt{2}$) of the total time; the second half takes the remaining 30%.

Answer 1

The Correct Option is C

Step 1: Concept
For free fall, $h = \frac{1}{2}gt^2$, so time $t \propto \sqrt{h}$.

Step 2: Meaning
Let $T_1$ be the time to fall $H/2$. Then $T_1 = \sqrt{\frac{2(H/2)}{g}}$ and $T = \sqrt{\frac{2H}{g}}$. Thus $T_1 = T/\sqrt{2}$.

Step 3: Analysis
The time taken for the second half is $T - T_1 = T - T/\sqrt{2}$.

Step 4: Conclusion
Factoring out $T$ gives $T(1 - 1/\sqrt{2}) = T(\frac{\sqrt{2}-1}{\sqrt{2}})$.
Final Answer: (C)