Three projecties A , B and C are projected at an angle of `30^(@)` , `60^(@)` respectively , If `R_(A)`, `R_(B)` and `R_(C)`are ranges of A, B and C respectively then (velocity of projection is same for A, B and C

Options

A. `R_(A)= R_(B)=R_(C)`
B. `R_(A)=R_(C)gtR_(B)`
C. `R_(A)lt R_(B)ltR_(C)`
D. `R_(A)=R_(C)ltR_(B)`

Answer

d

Explanation

Range , R = `(u^(2)sin2theta)/(g)`
Here g is constant and u is same for the projectiles A, B and C `therefore R alphasin2theta`
`RightarrowR_(A):R_(B):R_(c)=Sin60^(@):Sin90^(@),Sin120^(@)`
`R_(A):R_(B):R_(C)=(sqrt3)/(2):1:(sqrt3)/(2)=sqrt3:2:sqrt3`
Hence , `R_(A)=R_(C)ltR_(B)`