In 1865 more than 100 years before the first successful moon

In 1865, more than 100 years before the first successful moon mission, Jules Verne wrote the novel “From the Earth to the Moon,” in which three people are sent to the moon in a spacecraft shot from a large cannon. Let’s see whether this is actually a practical method of getting humans into space. Assume that the cannon has a barrel of length L, and that the acceleration in the barrel of the cannon is constant and equal to a. The spacecraft starts from rest, and its launch speed is vf.

a) Starting with the basic kinematic equations, derive an equation for the required acceleration (a) in terms of the length of the barrel and the launch speed.
b) In Verne’s story, the cannon had a barrel 210 m long and launched the spacecraft at 16.5 km/s (greater than the escape speed from Earth, 11.2 km/s, to allow for atmospheric friction). Use the equation from a) to find the magnitude of the acceleration the spacecraft (and its occupants!) would have experienced during the launch.
c) Compare this to the acceleration experienced by Air Force physician John Stapp, who in the 1950’s rode a rocket-propelled sled in order to test how much acceleration humans could survive. In his final run in December 1954, Stapp set a record for enduring large accelerations. His sled accelerated to 632 miles per hour in five seconds, then came to a stop in 1.4 seconds. During the stop, what magnitude of acceleration did he experience? Convert your answer to the same units you used in b) for easy comparison.
d) Based on your answers to the previous parts of this problem, do you think Verne’s launching method is feasible? Explain.

Solution

(A) length is L and launch speed is v.

initial speed = 0
then applying

vf^2 - vi^2 = 2 a d

v^2 = 2 a L

a = v^2 / 2 L

(B) a = (16.5 x 10^3 m/s)^2 / (2 x 210 m) = 648214.3 m/s^2

(c) v = u + at

v = 632 mph = 632 x 1609 m / 3600 s = 282.47 m/s

a = change in v / t = (282.47 - 0) / 1.4 = 201.76 m/s^2

(D) No, that acc was way more than human could survive.

ration = 648214.3 / 210.76 = 3075 times

That is not possible.