Two particls are projected in air with speed u at angles `theta_(1) and theta_(2)` (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct? where `T_(1) and T_(2)` are the time of flight.

Options

A. `theta_(1) gt theta_(2)`
B. `theta_(1) = theta_(2)`
C. `T_(1) lt T_(2)`
D. `T_(1) = T_(2)`

Answer

a

Explanation

Height `H=(u^(2) sin^(2) theta)/(2g)`
For the same speed
`H propsin^(2)theta`
`:'H_(1)gtH_(2)` (Given)
`:. Sin^(2) theta_(1)gt sin^(2) theta_(2)`
or `theta_(1) gt theta_(2)`....(i)
Time of flight, `T=(2u sin theta)/g`
For the same speed
`T prop sin theta`
`theta_(1) gt theta_(2)` (from(i))
`:. sin theta_(1) gt sin theta_(2) implies T_(1) gt T_(2)`