While on vacation in the tropical Bahamas, Suzy decides to try out a water jet pack. She places the jet pack on her back (like you would wear a backpack), pushes the buttons in her hands, and water comes shooting out of the bottom of the jetpack, exerting a force on the ocean below. Why does Suzy fly up into the air? In your answer, be sure to state which of Newton's laws of motion this pertains to, describe this law, and explain how it causes Suzy to fly up into the sky.

We know that in momentum, Force is described as the rate of change of momentum. Thus, for us to understand the forces, we will need to establish how the momentum of the water changes.

Suppose the mass flow rate of the water is denoted as M kg/sec and the upward velocity is denoted as v_u.

Now, since water is lying stationary at the sea, the initial momentum of the water will be zero. If every second the boat pumps upwards with mass flow rate M at velocity vu, the momentum per second would be;

Δp = F_water = Mv_u

Now, from Newton's third law the boat/pump would experience a downwards force with the formula:

F_boat = −Mv_u

Furthermore at the jetpack, the water does a reverse turn in direction and is now again directed back down at a different velocity v_d. Therefore the final momentum per second is Mv_d and therefore change in momentum is now;

Δp = M(v_d - v_u)

The velocity v_d will be negative since the boat/pump would experience a downwards force. Thus, the force on the water will be downwards and F_water ≤ 0 .

We will finally use Newton's third law to conclude that the upward force on the jetpack will be;

F_jetpack = M(v_u - v_d)

Thus upward force is what makes Suzy to fly up in the sky.