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?
vf^2=vi^2 + 2 a* distance.
change v to m/s
220
To determine the acceleration experienced by the passengers in Jules Verne's proposal, we can use the equations of motion. Specifically, we can use the kinematic equation that relates acceleration, final velocity, initial velocity, and displacement:
vf^2 = vi^2 + 2ad
Where:
- vf is the final velocity (11.31 km/s or 11,310 m/s in this case)
- vi is the initial velocity (which we assume to be 0 m/s in this case, as the capsule is initially at rest)
- a is the acceleration (what we're looking to find)
- d is the displacement (which, in this case, is not given)
Rearranging the equation gives us:
a = (vf^2 - vi^2) / (2d)
From the given information, we know that the length of the cannon is 207.9 m, but we don't have the exact displacement of the capsule. However, we can assume that the entire length of the cannon barrel is used as the displacement.
Substituting the given values into the equation, we have:
a = (11,310^2 - 0) / (2 * 207.9)
Simplifying the equation, we get:
a = 64,144,100 / 415.8
Calculating the result gives us:
a ≈ 154,411.22 m/s^2
Therefore, the passengers would experience an acceleration of approximately 154,411.22 m/s^2.