# Landing Rockets on Ships

SpaceX is trying to land their next reusable rocket back on a drone ship. The drone ship is traveling due west in an ocean current at a constant speed of $$5 \text{ m}/\text{s}$$. The rocket is $$2000 \text{ m}$$ east of the drone ship and $$5000 \text{ m}$$ vertically above it, traveling vertically downwards at $$100 \text{ m}/\text{s}$$. If the rocket can apply vertical and horizontal thrusts to change the acceleration of the rocket in the vertical and horizontal directions, and must accelerate constantly in both directions, find the magnitude of the net acceleration (vector) required to land on the ship with no vertical velocity. Answer in $$\text{ m}/\text{s}^2$$ to the nearest tenth.

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