A stone falls freely under gravity. It covered distances `h_1, h_2` and `h_3` in the first `5` seconds. The next `5` seconds and the next `5` seconds respectively. The relation between `h_1, h_2` and `h_3` is :

Options

A. ` h_1 = h_2 =h_23`
B. ` h_1 =2 h_2 =3 h_3`
C. ` h_1 = h_2/3 = h_3/5`
D. ` h_2 = 3 h_1 `amd ` h_3 = 3 h_2`

Answer

A

Explanation

Here, ` h_1 = 1/2 g (5)^2 = (250/2 g ,`
` (h-1 + h_2 ) = 1/2 g ( 5 +5 )^2 = 50 g`
`( h_1 + h_2 = h_3 ) =1/2 g ( 5 + 5 =5)^2 = (225)/2 g`
Now ` h_2 = (h_1 = h_2) - h_1 = 50 g- (25)/2 g`
` = ( 75)/2 g= 3 h_1`
or ` h_1 = _2/3 `
And ` h_3 = ( h_1 +h_2 + h_3 ) - ( h_1 + h_2)`
` = ( 225)/2 g - 50 = (125)/5 g = 5 h_1`
or ` h_1 = h_3 /5`
Chocie (c ) is correct .