Question

From street level, Superman spots Lois Lane in trouble. The evil villain, Lex Lutheor is dropping her from near the top of the Empire State Building. At the very instant, the man of steel starts upward at a constant acceleration to attempt a mid-air rescue of Lois. Assuming she was dropped from a height of $300m$ and the Superman can accelerate straight upward at $15m/s^2$. Determine how far Lois falls before he catches her.

• A. $300m$
• B. $120m$
• C. $150m$
• D. None of these

Answer 1

Answer: (B)

$120m$

Relative acceleration between Lois and Superman, $a=25m/s^2$.

Relative initial velocity, $u=0$

Relative initial distance, $h=300/m$

Let the time interval, after which the relative distance be zero, be $t$.

This means, after $ts$, Superman will catch Lois.

So, using second equation of motion, we get:

$300=0+\frac{1}{2}\times 25\times t^2$

$\Rightarrow$ $t^2=24$

Then, the height through which Lois falls before Superman catches her is:

$h=\frac{1}{2}\times g\times t^2=\frac{1}{2}\times 10\times 24=120$

$\therefore$ Lois falls through a height of $120m$ before Superman catches her.