Question

A body stats falling from height 'h' and travel distance h/2 during last sec of motion then time of travel ( in sec)

Answer 1

Given,

Time = t

height = h

The body covered h/2 distance in the last sec.

So,

when height is h,

h = 1/2 gt²

2h = gt²

h/2 distance has been cover in last sec = (t-1)

so, h/2 = 1/2 g (t-1)²

h = g (t-1)² divide both equations

2= t² / (t-1)² taking under rot on both sides

t/(t-1) =√2

$t=\sqrt{2}t-\sqrt{2}$

$\sqrt{2}t-t=\sqrt{2}$

$t(\sqrt{2}-1)=\sqrt{2}$

$t=\frac{\sqrt{2}}{\sqrt{2}-1}X\frac{(\sqrt{2}+1)}{(\sqrt{2}+1)}$

$t=\frac{(2+\sqrt{2})}{2-1}=2+1.41=3.41$