Junes Verne in 1865 suggested sending people to the Moon by firing a space capsule from a 255 m long cannon with a launch speed of 11.42 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during launch?

Question

Compare your answer with the free-fall acceleration 9.80 m/s2

Answer 1

0 to 11,420 m/s in 255 meters
acceleration = a

velocity = a t
so 11,420 = a t
t = 11,420/a

distance = (1/2) a t^2
so
255 = (1/2) a (11,420^2/a^2)
510 a = 11,420^2
a = 255,718 m/s^2
a/g = 26,093 times the acceleration of gravity
ouch, much better to use a rocket and get up to escape speed more slowly.