IIT JEE , AIEEE Forum - Physics , Mechanics

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For the ball thrown up
-h = ut₁ - (1/2)gt₁²
h = -ut₁ + (1/2)gt₁² --------(1)

For the ball thrown down
-h =- ut₂ - (1/2)gt₂²
h = ut₂ + (1/2)gt₂² --------------(2)

For the freely falling ball
-h = - (1/2)gt² -----------(3)

Multiply (1) by t₂ & (2) by t₁ and add
h(t₁ + t₂) = (1/2)gt₁t₂ ((t₁ + t₂)
Cancelling (t₁ + t₂) and substituting the value of h from (3)
(1/)gt² = (1/2)gt₁t₂
t =

t₁t₂

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