Show that there are two values of time for which a projectile is at the same height. Also show mathematically that the sum of these two times is equal to the time of flight.

Explanation

In angular projection of a projectile, let (h) the height attained by projectile in timings ` t_1 and t_2` respetively, Then
`h=u sin theta t_1 - 1/2 g t_1 ^2 =u sin theta t_2 - 1/2 g t_2 ^2`
or (u) ` sin theta (t_2 -t_1 ) = 1/2 g (t_2 ^2 - t_1 &2)`
`= 1/2 g (t_2 -t_1 ) (t_2 + t_1)`
or ` (t_2 + t_2) =(2 u sin theta)/g = total time of flight .