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 back

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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 back

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A stone thrown vertically upwards with initial velocity' u' reaches a ...

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-1/2gt^2 -----------(2)

v^2-u^2=-2gh --------(3)

Equations of motion for freely falling body :

for free fall :

Initial velocity=u=0

g=g

V=gt----------(4)

h=1/2gt^2-------(5)

v^2=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=u^2/2g ----------(8)

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

so equation (5) h=1/2gt₂^2

t₂^2=2h/g

t₂=√2h/g

but from equation (9)

t₂=√2xu^2/2g^2

t₂=u/g -------equation (10)

∴t₁=t₂

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

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