At `t = 0` a projectile is projected vertically up with a speed u from the surface of a peculiar planet. The acceleration due to gravity on the planet changes linearly with time as per equation `g = alphat` where `alpha` is a constant.
(a) Find the time required by the projectile to attain maximum height.
(b) Find maximum height attained.
(c) Find the total time of flight.

Answer

(a) `t_(0) = sqrt((2u)/(alpha))` (b) `((2u)^(3//2))/(3alpha^(1//2))`
(c) `sqrt((6u)/(alpha))`