We use our superior intelligence and specifically our knowledge of kinematics to shoot this monkey. The setup works as follows. At t=0 we fire a projectile and the monkey is released from the top of this stick. The question is how should we aim the air-gun in order for the projectile to hit the monkey?
It is clear that everything goes on in a plane. All we need to figure
out is the angle, 
, of elevation of the air-gun. We follow the same
strategy as in the previous problem. We write the position vector of
the projectile 
and the position vector of the
monkey, 
and look for a time where the location
of the poor monkey coincides with that of the projectile.
In writing the position vectors we choose the origin to be the
location of the projectile in the air-gun at t=0. Our coordinate
system is naturally that with the 
axis horizontal and the 
axis pointing straight up. We have
For the monkey we have
Here we denote 
the location of the monkey at time t=0.
Impact occurs when
This vector equation is satisfied when both the corresponding coordinate
equations are simultaneously satisfied ie.
The quadratic term cancels out to leave us with much simpler equations
dividing the second equation with the first we obtain
Notice that this equation relates the launch angle, with the
angle, 
between the line from gun to monkey at t=0
and the horizontal direction. Specifically
which means that we shall hit the monkey if we point our gun directly at it
before firing. We try it and hopefully we actually do hit the monkey.
In words what happens here is that the vertical free fall of the monkey
exactly equals the free fall of the projectile as it propagates toward
the monkey.