# Landing Rockets on Ships

**Classical Mechanics**Level 3

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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