2-15. A bullet hits a
block at rest at a horizontal speed 
and exits the block at
speed 
. Both speeds and are measured and
treated as random variables due to the measurement uncertainty. They are
independently distributed with 
and 
. The mass of the bullet and the wooden block are 
and 
, respectively. The coefficient of kinetic friction between
the block and floor is 
. How long does the block slide on the floor before it comes
to rest again?
Solution:
Conservation
of linear momentum
After
the bullet exits the block, the only force acts on the block in 
-direction is the friction force, from the free-body diagram,
we have
When
the block comes to rest again, 
.
Principle
of impulse and momentum of the block:
Therefore, 
.
Ans.