A bullet is fired straight up. Neglecting air resistance, the speed of the bullet when it falls back down is

The speed of the bullet at the time of strike to the earth is same as the initial speed with which it is fired.

Explanation:

Let the initial speed of the bullet is u.

The maximum height attained by the bullet is H.

As there is no friction, so according to the conservation of energy,

Kinetic energy at the bottom = Potential energy at the top  =Kinetic energy at the bottom again  

So, the speed of the bullet as it reaches the earth again is same as the initial velocity = u .