If air resistance in neglected, show (algebraically) that a ball thrown vertically upwards with a speed of vo will have the same speed, vo, when it comes back down to starting point.

Explanation:

If the air resistance is negligible then in that case we can say that there will be only one force on the ball

Force of gravity

so here we will have

so the acceleration of the ball is given as

now we have

as the ball returns to initial position

so the displacement must be zero

so here we have