The Poacher Problem

So recently I have come across a beautiful problem, this is a very well known one to anybody that has taken a first-year University Dynamics and or Mechanics course.
NOTE: There have been no monkeys hurt in the creation of this blog post.
So let us consider a monkey sitting in a tree, a poacher is wanting to shoot this very rare and exotic monkey! He primes and aims his gun… the monkey releases his hold of the tree and starts falling… BANG!
Is the monkey dead?

This is the set up for the problem, so we can now look into the Mathematics behind this, to do so we shall need to go through some prerequisites:

Inertial Frames

An inertial frame is a mathematical object that is used to study a dynamical system. Intuitively we can use it to cancel equal forces that are happening to similar objects. In this problem, we shall treat the monkey and bullet as point particles and so they are similar. It is usually done using a change of coordinates

Now, taking this definition of an inertial frame, create one where everything is accelerated upwards with acceleration g ≈ 9.81. This should now stop anything from accelerating downwards, hence negating the effect of gravity. Note as we have done the same thing to the two objects, then whatever happens in this reference frame will happen to everything in the original reference frame.
Now, let go back to the setup of the question and press play from where the monkey lets go. The monkey doesn’t fall anymore and neither would the bullet of the gun. This means as long as the poacher aims his gun at the monkey, it’s dead.

Thinking about this logically, we can look at the situation and solve the problem without inertial frames. We know, things fall at the same rate under gravity, regardless of weight. So we have a monkey and a bullet gravelling towards each other, on the same path downwards. They must hit, the only thing that could happen is one misses the other as its travelling too quickly, but we know the monkey comes from rest and then the bullet is given a dramatic impulse of energy, so then the only two forces acting on the two would be gravity. Then they must collide.

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