Junes Verne in 1865 suggested sending people to the Moon by firing a space capsule from a 255 m long cannon with a launch speed of 11.42 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during launch?
Compare your answer with the free-fall acceleration 9.80 m/s2
0 to 11,420 m/s in 255 meters
acceleration = a
velocity = a t
so 11,420 = a t
t = 11,420/a
distance = (1/2) a t^2
so
255 = (1/2) a (11,420^2/a^2)
510 a = 11,420^2
a = 255,718 m/s^2
a/g = 26,093 times the acceleration of gravity
ouch, much better to use a rocket and get up to escape speed more slowly.
To find the acceleration experienced by the space travelers during launch, we can use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
In this scenario, the initial velocity is 0 (since the capsule starts from rest), and the final velocity can be found using the launch speed given in the question (11.42 km/s).
To convert the launch speed from km/s to m/s, we multiply it by 1000:
launch speed = 11.42 km/s * 1000 = 11420 m/s.
Now we can calculate the acceleration:
acceleration = (11420 m/s - 0) / time
To determine the time it takes for the capsule to be launched, we need to know the distance the capsule covers. The question provides the length of the cannon, which is 255 m. However, we need additional information to calculate the time.
Unfortunately, the question does not provide the time taken for the capsule to travel the 255 m. Without this information, we cannot determine the acceleration.