Question

Prove that the distance travelled during equal intervals of time by body falling from rest stand to one another in the same ratio as the odd numbers beginning with unity

Answer 1

1 answer · Physics

Best Answer

u = 0

in the first interval t :

=> v = 0 + gt = gt

h1 = 0 + 1/2 gt^2 = 1/2 gt^2 --- (1)

.. for the second interval t : => v2 = v + gt = gt + gt = 2gt

h2 = vt + 1/2 gt^2 = gt^2 + 1/2 gt^2 = 3/2 gt^2 --- (2)

.. for the 3rd interval t :=> v3 = v2 + gt = 2gt + gt = 3gt

=> h3 = v2t + 1/2 gt^2 = 2gt^2 + 1/2 gt^2 = 5/2 gt^2 --- (3)

and .. for the 4th interval t :

=> h4 = v3t + 1/2 gt^2 = 3gt^2 + 1/2 gt^2 = 7/2 gt^2 --- (4)

now if u find the ratio h1 : h2 : h3 : h4 u get :

1/2 gt^2 : 3/2 gt^2 : 5/2 gt^2 : 7/2 gt^2

by cancelling 1/2gt^2 u get the ratio :

1 : 3 : 5 : 7

hope it's clear