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.

Answer

A

Explanation

For vertically upward motion of a projectile,
`y=(u sin alpha)t - 1/2 (g t^2) or 1/2 g t^2 -(usin alpha)t+y=0`
This is a quadratic equation in t. Its roots are
`t_(1)=(u sing alpha-sqrt(u^(2)sin^(2)alpha-2gy))/(g)`
and `t_(2)=(us sin alpha+sqrt(u^(2)sin^(2)alpha-2gy))/(g)`
`:. t_(1)+t_(2)=(2u sin alpha)/(g)=T` (time of flight of the projectile).