d. A stone thrown vertically upwards witinitial velocity u reaches a h

1.	d. A stone thrown vertically upwards witinitial velocity u reaches a height 'h'before coming down. Show that thetime taken to go up is same as the timetaken to come down.
Answer» 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=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 hAt 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=1/2gt₂²t₂²=2h/gt₂=√2h/gbut from equation (9)t₂=√2xu²/2g²t₂=u/g -----------------equation (10) ∴t₁=t₂ The time ascent is equal to time of descent in case of bodies moving under gravity. thank you

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

Answer»

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=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 hAt 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=1/2gt₂²t₂²=2h/gt₂=√2h/gbut from equation (9)t₂=√2xu²/2g²t₂=u/g -----------------equation (10)

∴t₁=t₂

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

thank you