Question

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

Answer 1

I have not reached the state yet else I would like to tell whatever you need

Answer 2

Let us consider an object which is projected vertically upwards with initial velocity  u which reaches a maximum height h.

Acceleration due to gravity=-g

Equation 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=0

g=g

V=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=gt1

t1=u/g  ----------(7)

Maximm height h=u²/2g ----------(8)

Time of descent : After reaching maximum height , the body begins to travel downward like free fall

so equation (5) h=1/2gt₂²

t₂²=2h/g

t₂=√2h/g

but from equation (9)

t₂=√2xu²/2g²

t₂=u/g -----------------equation (10)

∴t₁=t₂

The time ascent is equal to time of descent in case of bodies moving under gravity.

hope it helps