Two particles are projected from ground with same intial velocities at angles `60^(@)` and `30^(@)` (with horizontal). Let `R_(1)` and `R_(2)` be their horizontal ranges, `H_(1)` and `H_(2)` their maximum heights and `T_(1)` and `T_(2)` are the time of flights.Then

Options

A. `H_(1)/R_(1)gtH_(2)/R_(2)`
B. `H_(1)/R_(1)ltH_(2)/R_(2)`
C. `H_(1)/T_(1)gtH_(2)/T_(2)`
D. `H_(1)/T_(1)ltH_(2)/T_(2)`

Answer

A, C

Explanation

At `30^(@)` and `60^(@)`,`R_(1)R_(2)`
Further,`H prop sin^(2) theta` and `T prop sin theta`
`:.H/R prop sin^(2) theta` and `H/T prop sin theta`
`sin 60^(@) gt sin 30^(@)`
`:. H_(1)/R_(1) gt H_(2)/R_(2)` and `H_(1)/T_(1) gt H_(2)/T_(2)`