Physics
posted by Tarbela Damme on .
Neglect the gravity of the Moon, neglect atmospheric friction, and neglect
the rotational velocity of the Earth in the following problem. A
long time ago, Jules Verne, in his book From Earth to the Moon (1865),
suggested sending an expedition to the Moon by means of a projectile
fired from a gigantic gun.
(a) With what muzzle speed must a projectile be fired vertically from a
gun on the surface of the Earth if it is to (barely) reach the distance of
the Moon?

Using the radius of the Earth and Moon as 3963 miles and 1080 miles, respectively, and the distance between them as 239,000 miles, the surface to surface distance becomes 233,960 miles.
From Vf^2 = Vo^2  2gs, 0 = Vo^2  2(32.2)233,960 or Vo = 282,053 fps = 192,309 mph.
The trip time then becomes t = 282,053/32.2 = 8760 sec = 2hr26min.
Theoretically, the liftoff velocity should be 192,310 mph.