In 1865, Jules Verne suggested sending people to the Moon by launching a space capsule with a 228.8 m long cannon. The final speed of the capsule must reach 11.39 km/s. What acceleration would the passengers experience?
Acceleration a from rest over a distance of S to a velocity of v is given by:
v²=2aS
or
v=11390 m/s
S=228.8m
a=v²/(2S)
=11390²/(2*228.8) m/s²
=283,505 m/s²
=28,929 g
Jules Verne had correctly calculated the escape velocity on planet earth, which is the velocity required for an object to leave earth's gravitation system without further propulson.
However, his suggestion did not include cases where propulsion could be continuous, in which case the acceleration can be much reduced.
To calculate the acceleration experienced by the passengers in Jules Verne's scenario, we can use the formula for acceleration:
acceleration = final velocity^2 / (2 * displacement)
In this case, the final velocity is given as 11.39 km/s, but we need to convert it to m/s.
To convert km/s to m/s, we multiply by 1000 (since there are 1000 meters in a kilometer):
final velocity = 11.39 km/s * 1000 = 11390 m/s
Now, we need to find the displacement. The displacement is the distance covered by the capsule, which is given as the length of the cannon: 228.8 m.
Substituting the values into the formula:
acceleration = (11390 m/s)^2 / (2 * 228.8 m)
Calculating this:
acceleration = 129504100 / 457.6
acceleration ≈ 283093.02 m/s²
Therefore, the acceleration experienced by the passengers would be approximately 283093.02 m/s².