Question

Help Please!! An object is dropped from a height h meters. From the time the object is h/2 meters above the ground, it takes 1 second until the object strikes the ground. From what height was the object dropped?

Answer 1

Here object is dropped from height "h"

so we can say its initial speed is zero

and it will accelerate downwards due to gravity

now we can say it will take time T to hit the ground

now we can use

$h = v_i*t + \frac{1}{2}gt^2$

$h = 0 + \frac{1}{2}*gT^2$

now it is given that it will take 1 second to drop h/2 height to strike the ground

so here we have can say that in "T - 1" s it will cover the h/2 distance from start

$h/2 = 0 + \frac{1}{2}g(T-1)^2$

now we can say

$h = g(T-1)^2$

from above two equations we have

$\frac{1}{2}gT^2 = g(T-1)^2$

$T^2 = 2(T^2 + 1 -2T)$

$T^2 - 4T + 2 = 0$

$T = 3.41 s$

now we can find total height of the drop by first equation

$h = \frac{1}{2}gT^2$

$h = \frac{1}{2}*9.81*3.41^2$

$h = 57.2 m$