### Video Transcript

A bullet was fired horizontally
at a wooden block. It entered the block at 80
meters per second and penetrated 32 centimeters into the block before it
stopped. Assuming that its acceleration
𝑎 was uniform, find 𝑎. If under similar conditions,
another bullet was fired at a wooden block that was 14 centimeters thick,
determine the velocity at which the bullet exited the wooden block.

In our first scenario, we are
told that a bullet is fired with velocity 80 meters per second. It penetrates 32 centimeters
into the block. And as there are 100
centimeters in one meter, this is equal to 0.32 meters. To calculate the value of 𝑎,
we will use the equations of uniform acceleration or SUVAT equations. We know that 𝑠, the
displacement or distance, is equal to 0.32 meters, the initial velocity is 80
meters per second, the final velocity is zero meters per second, and we are
trying to calculate the acceleration 𝑎. We will do this using the
equation 𝑣 squared is equal to 𝑢 squared plus two 𝑎𝑠.

Substituting in our values
gives us zero squared is equal to 80 squared plus two 𝑎 multiplied by 0.32. This simplifies to zero is
equal to 6400 plus 0.64𝑎. We can then subtract 6400 from
both sides and then divide by 0.64. This gives us a value of 𝑎
equal to negative 10000. The acceleration of the bullet
is negative 10000 meters per second squared. As there are 1000 meters in a
kilometer, this can also be written as negative 10 kilometers per second
squared.

In our second scenario, the
bullet travels straight through a wooden block of thickness 14 centimeters or
0.14 meters. Using the same values of 𝑢 and
𝑎, we can now calculate 𝑣, the velocity, at which the bullet exits the wooden
block. We know that 𝑣 squared is
equal to 𝑢 squared plus two 𝑎𝑠. Substituting in our values, we
can calculate 𝑣 squared. This is equal to 3600. Square rooting both sides and
knowing that 𝑣 must be positive, we get 𝑣 is equal to 60. The bullet exits the block at a
velocity of 60 meters per second.