the questions are the specific impulse of those engines, then Delta-V.

a mentos and coke can reach about 3m height gayser, therefore initial nozzle velocity is 7.67m/s, and a 2l bottle lasts about 2 seconds. resulting in a ISP of 0.7822 seconds.

for comparison, the shuttle solid rocket booster has an isp of 250 seconds, a normal liquid rocket engine is about 450 seconds (the more the better).

plugging in the weights of the Saturn 1, gives a delta V of [drumroll] 18.6 m/s… enough to accelerate a giant rocket to highway speeds.