Two particles are projected from the same point on ground simultaneously with speeds and `20m//s and 20//sqrt3` at angles `30^(@)` and `60^(@)` with the horizontal in the same direction.The maximum distance between them till both of them strike the ground is approximately `(g=10m//s^(2))`

Options

A. `23.1 m`
B. `16.4 m`
C. `30.2 m`
D. `10.4 m`

Answer

A

Explanation

Components of velocities of both the particles in vertical direction are equal.Therefore, their time of flights are equal and their relative motion is in horizontal direction only.Thus, the maximum distance between them is equal to the difference in their horizontal ranges.
`R_(1)((20)^(2) sin 60^(@))/g=((400)sqrt3)/(10xx2)=34.64 m`
`R_(2)=((20/sqrt3)^(2) sin 120^(@))/g=(400xxsqrt3)/(10xx3xx2)=11.55 m`
`:. S_(max)=34.64-11.55=2309m=23.1m`