Can anyone help me with this problem?

A bullet of mass m is moving horizontally with speed Vo when it hits and embeds in a block of mass 100m that is at rest on a horizontal frictionless table (in the diagram it isn't placed at the edge of the table, i don't know if this matters). The surface of the table is a height h above the floor. After the impact the bullet and the block slide off the table and hit the floor a distance x from the edge of the table.

Derive expressions for the following quantities in terms of m, h, Vo and appropriate constants.
a.) the speed of the block as it leaves the table
b.) the change in kinetic energy of the bullet-block system during the impact
c.) the distance x

Suppose that the bullet passes through the block instead of remaining in it.
d.) state whether the time it takes the block to reach the floor from the edge of the table would now be greater, less, or the same
e.) state whether the distance x would now be greater, less, or the same


Thanks for any help!

a) speed of the block as it leaves the table

m*Vo = (101m)*v_block : Conservation of momentum

v_block = Vo / 101 : Division


the change in kinetic energy of the bullet-block system during the impact

Change in K = K_f - K_i

1/2*m*Vo^2 - 1/2*101m*(Vo / 101)^2


Simplify to get (50/101)*m*Vo^2 Joules


c) the distance x

First find how long the block falls for:

0 = h - 1/2*9.8*t^2 : Kinematic equation

t = sqrt(h / 4.9)

Now find how far the block traveled horizontally (x) in that time

x = (Vo / 101)*sqrt(h / 4.9) : Kinematic equation


d) Since gravity is the same, it would would take the same amount of time to fall to the floor

e) Intuitively, I'd say that would travel less (although intuition often misleads in physics).