Question

A ball 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 ?

Answer 1

Option A

`(V)/(√(2) )` ,
`(E)/(2)`

Step-by-step explanation:

When the ball its thrown up, at half way of its flight it means half of its vertical height which is
`(h)/(2)`.

potential energy = mgh

since it moved half way of height

P.E =
`(mgh)/(2)`

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_(1)`) = E/2

kinetic energy =
`(1)/(2)mv^(2)`

let the final velocity at halfway flight be v1

`E_(1)` = E/2

`(1)/(2)mv_(1)^(2)` =
`((1)/(2)mv^(2))/(2)`

cross multiply we have

`mv_(1)^(2)` =
`(1)/(2)mv^(2)`

cancel m from both sides

`v_(1)^(2)` =
`(1)/(2)v^(2)`

take the square root of both sides,

`v_(1) =\sqrt{(v^(2) )/(2) }`

`v_(1) =(v)/(√(2) )`

Thus our final velocities will be E/2 and
`(v)/(√(2) )`