Junes Verne in 1865 suggested sending people to the Moon by firing a space capsule from a 195 m long cannon with a launch speed of 12.78 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during launch?
____ m/s^2
It is the acceleration a that you get by requiring that V^2 = 2 a X
V is the launch vecloity and X = 195 m
To find the acceleration experienced by the space travelers during launch, we can use the kinematic equation:
v^2 = u^2 + 2aS
Where:
v = final velocity (12.78 km/s)
u = initial velocity (0 m/s, assuming the capsule starts from rest)
a = acceleration (what we're trying to find)
S = distance traveled (195 m)
Rearranging the equation:
a = (v^2 - u^2) / (2S)
Now let's substitute the given values and calculate the acceleration:
v = 12.78 km/s = 12,780 m/s
u = 0 m/s
S = 195 m
a = (12,780^2 - 0^2) / (2 * 195)
Calculating:
a = 163,368,900 / 390 = 419,695.38 m/s^2
Therefore, the acceleration experienced by the space travelers during launch would have been approximately 419,695.38 m/s^2.