How can you make simple electric rocket?

Answer 1

1. Get a paper towel/toilet paper roll.

2. Make some sort of guidance system... like a straw taped to it, or 3 paper fins on the sides.

3. Put (mint only) Mentos is the paper towel/toilet paper roll and tape a piece of paper to the bottom.

4. Put the rocket in a large cup full of Diet Coke/ Regular Coke.

5. Congratulations! You just made yourself a homemade rocket!

6. Stand back and watch it fly!

Answer 2

You can't because a rocket works by the force reaction to a powerful jet of expelled gas.

A projectile can be built (if you have the design and manufacturing expertise) that uses linear motors to accelerate it along a rail, but once the projectile leave the rail and magnetic windings its flight is purely ballistic.

It's also possible to construct an ion rocket. One was built and is in use for the space probe Dawn. These work by using an electric field to accelerate charged ions. Ion propulsion has a low specific thrust, but they allow for long thrust times since the reaction mass is separate from the power generator. (Dawn was launched with a conventional chemical propulsion system, and only used the ion drive once it was largely out of Earth's gravity well.)

This isn't a "simple" rocket, though, the nuclear reactor to generate power is probably the easy part.