A body is projected from the ground at an angle of `tan^(-1) ((8)/(7))` with the horizontal. The ratio of the maximum height attained by it to its range is

Options

A. `8:7`
B. `4:7`
C. `2:7`
D. `1:7`

Answer

C

Explanation

For a projectile projected at angle `theta`, Maximum height, `H_("max") =(u^(2) sin^(2) theta)/(2g)`
and range, `R =(u^(2) sin 2 theta)/(g)`
`therefore" Ratio "=(H_("max"))/(R ) =(((u^(2)sin^(2) theta)/(2g)))/(((u^(2) sin 2 theta)/(g)))= (tan theta)/(4)`
Here, `theta = tan^(-1) (8)/(7) rArr tan theta =(8)/(7)==((8)/(7))/(4)=(2)/(7)`