In 1865, Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10.97 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of 15g for a short time.)
Compare your answer with the free-fall acceleration, 9.80 m/s2 (i.e. how many times stronger than gravity is this force?).
change 10.97km/s to 10970m/s geepers that is fast.
vf^2=vi^2+2ad
a=1/2 (10979)^2 /(220*9,8) g's
27908.37
To solve this problem, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (10.97 km/s)
u = initial velocity (0 m/s)
a = acceleration (unknown)
s = distance (220 m)
Rearranging the equation to solve for acceleration, we have:
a = (v^2 - u^2) / (2s)
Now we can substitute the given values:
a = (10.97 km/s)^2 / (2 * 220 m)
Converting the velocity from km/s to m/s:
a = (10.97 × 1000 m/s)^2 / (2 * 220 m)
Simplifying the equation:
a = 1201049 m^2/s^2 / 440 m
a = 2738.75 m/s^2
Now we can compare this acceleration to the free-fall acceleration of 9.80 m/s^2:
2738.75 m/s^2 / 9.80 m/s^2 = 279.89
Hence, the acceleration experienced by the space travelers during launch would be approximately 279.89 times stronger than gravity.
To find the unrealistically large acceleration experienced by the space travelers during their launch, we can start by using the basic equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (10.97 km/s or 10970 m/s)
u = initial velocity (0 m/s, as the capsule starts from rest)
a = acceleration
s = displacement (220 m, as the cannon is 220 m long)
Rearranging the equation, we can solve for the acceleration (a):
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (10970^2 - 0^2) / (2 * 220)
Calculating this expression, we get:
a ≈ 2704286 m/s²
So, the unrealistically large acceleration experienced by the space travelers during their launch would be approximately 2,704,286 m/s².
Now, to compare this acceleration with the free-fall acceleration (9.80 m/s²):
The unrealistically large acceleration is approximately 2,704,286 / 9.80 ≈ 275,876 times stronger than the force of gravity.