In 1842, Julius Robert Mayer discovered The law of conservation of Energy. It its most compact form, it it now called The first law of Thermodynamics
Energy can neither be created nor destroyed, it can only be changed to another form of energy.
See if you get the answer with this formulae.
Question: How fast was the arrow moving before it joined the block?
Answer:
The arrow was moving at 15.9 m/s.
Explanation:
The law of conservation of energy says that the kinetic energy of the arrow must be converted into the potential energy of the block and arrow after it they join:

where
is the mass of the arrow,
is the mass of the block,
of the change in height of the block after the collision, and
is the velocity of the arrow before it hit the block.
Solving for the velocity
, we get:

and we put in the numerical values
,



and simplify to get:

The arrow was moving at 15.9 m/s