Jules Verne in 1865 suggested sending people to the Moon
by firing a space capsule from a 220-m-long cannon with a
launch speed of 10.97 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.
You can do this.
Change 10.97km/s to m/s
Then, Vf^2=2ad solve for a.
To determine the acceleration experienced by the astronauts during launch, we need to use the basic equation of motion:
v^2 = u^2 + 2as
Where:
- v is the final velocity (launch speed) = 10.97 km/s = 10,970 m/s
- u is the initial velocity (0 m/s since the travelers start from rest in the cannon)
- a is the acceleration experienced by the travelers
- s is the displacement or distance traveled by the travelers in the cannon = 220 m
Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)
Plugging in the values, we have:
a = (10,970^2 - 0^2) / (2 * 220)
Simplifying this calculation, we get:
a = 60,400,900 m^2/s^2 / 440
a = 137,733.4 m/s^2
Therefore, the unrealistically large acceleration experienced by the space travelers during launch would be 137,733.4 m/s^2.
Comparing this with the free-fall acceleration on Earth, which is approximately 9.80 m/s^2, we can see that the acceleration experienced during launch is significantly larger.