What you’re describing is the Sinclair C5 :-)

Look on YouTube for “gas turbine sinclair C5" :-)

How about my hybrid Gas-Turbine Electric Sinclair C5... Yes, really !! :-)

Each turbojet is 100 HP, not 1000 HP. A 75kW (100 HP) turbojet can output about 300N of thrust, thus 4 of these will give you 1200N of thrust. Enough to lift someone.