Aball is thrown vertically upwards with a velocity v and an initial kinetic energy ek. when half way to the top of its flight, it has a velocity and kinetic energy respectively of (a) v/square root 2, e/2 (b) v/4, e/2 or (c) v/2, e/square root 2 ?

Option A

,

Explanation:

When the ball its thrown up, at half way of its flight it means half of its vertical height which is .  

potential energy = mgh

since it moved half way of height

P.E =

This means for the body to have gained half of its P.E, it will loose half of its kinetic energy.

Final kinetic energy() = E/2

kinetic energy =

let the final velocity at halfway flight be v1

= E/2

=

cross multiply we have

=

cancel m from both sides

=

take the square root of both sides,

Thus our final velocities will be E/2 and

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