Question

During a blackout, you are trapped in a tall building. you want to call rescuers on your cell phone, but you can't remember which floor you're on. you pry open the doors to the elevator shaft, drop your keys down the shaft, and hear them hit bottom at ground level 3.27 s later. assume that the height of one floor is 3.0 m.

Answer 1

Let the height where we are trapped is H

now to find the time to reach the key at the bottom is given as

$y = v_i t + \frac{1}{2}at^2$

now we have

$H = \frac{1}{2}gt^2$

$t = \sqrt{\frac{2H}{g}}$

now if the speed of sound is considered to be 340 m/s then time taken by the sound to reach at the top is given as

$t = \frac{H}{340}$

now the total time is given as

$\sqrt{\frac{2H}{g}} + \frac{H}{340} = 3.27$

now by solving above equation we have

H = 48 m

now height of one floor is 3 m

so our position must be

$N = \frac{48}{3} = 16 th \:floor$