Question

A stone thrown vertically upwards with initial velocity u reaches a height h before comming down . Show that the time taken to go up is same as the time taken to come down.

Answer 1

Let us consider an object which is projected vertically upwards with initial velocity  u which reaches a maximum height h.Acceleration due to gravity=-gEquation of Motion for a body projected thrown upwards :V=u-gt----------(1)h=ut-1/2gt² -----------(2)v²-u²=-2gh --------(3)
Equations of motion for freely falling body :for free fall : Initial velocity=u=0g=gV=gt----------(4)h=1/2gt²-------(5)v²=2gh------(6)Time of Ascent is the time taken by body thrown up to reach maximum height h At maximum height , V=0
Equation (1) turns to u=gt1t1=u/g  ----------(7)Maximm height h=u²/2g ----------(8)
Time of descent : After reaching maximum height , the body begins to travel downward like free fallso equation (5) h=1/2gt₂²t₂²=2h/gt₂=√2h/gbut from equation (9)t₂=√2xu²/2g²t₂=u/g -----------------equation (10)∴t₁=t₂The time ascent is equal to time of descent in case of bodies moving under gravity.