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Question

A ball is thrown vertically upwards. Prove that its time of ascent is equal to the time of descent.


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Solution

Step 1: Given data

Final velocity during ascent v=0.

Initial velocity during descent u=0.

Acceleration during ascent a=-g.

Acceleration during descent a=g.

Step 2: Formula for calculating the time of journey

v=u+atwhere,vFinalvelocityuInitialvelocityaAccelerationtTime

Step 3: Calculating the time of ascent

v=u+att=v-uatascend=0-u-gtascend=ug

Step 4: Calculating the time of descent

v=u+att=v-uatdescent=v-0gtdescent=vgv=u

Step 5:Proving tascent=tdescent
For a body that is thrown upwards, v=u.

Thus, tascent=tdescent.

Hence, for a ball that is thrown vertically upwards, the time of ascent is equal to the time of descent.


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