Question

A stone falls freely under gravity. It covers distances h1, h2 and h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h1, h2 and h3 is:
A)

B)

C)

D)

plz tell the formula used .

Answer 1

A stone falls freely under gravity .
so, initial velocity of Stone, u = 0
use formula , s = ut + 1/2at²
then, -h1 = 0 - 1/2g(5)²
h1 = 125m .......(i)

let v is the velocity after 5 second.
then, v² = u² + 2as
v² = 0 + 2(-g)(-125)
v² = 2 × 10 × 125 = 2500
v = -50 m/s {negative sign show body falling downward}

now, stone covered h2 distance in next 5 second .
so, initial velocity of stone in this case ,u' = v = -50m/s
now, use formula, S = ut + 1/2at²
-h2 = -50 × 5 - 1/2 × 10 × 5²
-h2 = 250 + 125 = 375 m ......(ii)

velocity of stone , v' = u' + at
= -50 -10 × 5 = -150 m/s
now, stone covered h3 distance in next 5 second.
so, initial velocity of stone in this case ,u" = v' = -150m/s
use formula , S = ut + 1/2at²
-h3 = -150 × 5 - 1/2 × 10 × (5)²
h3 = 750 + 125 = 875 ......(iii)

from equations (i), (ii) and (iii),
h2 = 3h1 and h3 = 7h1
or, h1 : h2 : h3 = 1 : 3 : 7

Answer 2

Answer is

h1 = h2/3 = h3/5