In 1865, Jules Verne suggested sending people to the Moon by launching a space capsule with a 207.9 m long cannon. The final speed of the capsule must reach 11.31 km/s. What acceleration would the passengers experience?
The average speeed in the cannon is Vav = V/2 (where V is the exit velocity), and the time the capsule takes to leave the barrel is t = L/Vav = 2L/V
The acceleration rate a is V/t =
a = V^2/(2L)
To calculate the acceleration experienced by the passengers in Jules Verne's hypothetical scenario, we can use the equations of motion. We'll need to find the initial velocity, final velocity, and displacement of the capsule.
First, let's find the initial velocity. We know that the capsule is launched from rest, so the initial velocity (v0) is 0 m/s.
Next, let's find the final velocity (vf). We are given that the final speed of the capsule must reach 11.31 km/s. To convert this to meters per second, we can multiply it by 1000 and divide by 3600 (since there are 1000 meters in a kilometer and 3600 seconds in an hour):
vf = (11.31 km/s) * (1000 m/km) / (3600 s/h) = 3137.5 m/s
Now, let's calculate the displacement (s) of the capsule. The displacement is simply the length of the cannon, which is given as 207.9 m.
s = 207.9 m
To calculate the acceleration, we can use the following equation of motion:
vf^2 = v0^2 + 2as
Substituting the given values, we have:
(3137.5 m/s)^2 = (0 m/s)^2 + 2a * (207.9 m)
Simplifying the equation, we can solve for acceleration (a):
a = (vf^2) / (2s)
Plugging in the values:
a = (3137.5 m/s)^2 / (2 * 207.9 m)
Solving this equation gives the acceleration experienced by the passengers in the capsule.