Four bodies P, Q, R and S are projected with equal velocities having angles ofprojection `15^(@)`, `30^(@)`, `45^(@)` and `60^(@)` with the horizontal respectively. The body having shortest range is

Options

A. P
B. Q
C. R
D. S

Explanation

Speed at maximum height,`s=ucostheta`
`impliessqrt3/2u=ucostheta`
`impliessqrt3/2=costheta` ( `:.` u-Initial speed)
`impliestheta=30^(@)`
R=PH,
`implies(u^2sin2theta)/g=P[(u^2sin^2theta)/(2g)]`
`impliessin2theta=P/2xxsin^2thetaimpliessin60^0=P/2xxsin^2(30)impliessqrt3/2=P/2xx1/2xx1/2`
`:.P=4sqrt3m`