Thus, a body falling from a state of rest acquires a velocity to pass through 9 spaces in the fifth second of time; 7 in the fourth; 5 in the third; 3 in the second; and 1 in the first. Thus it is 9 + 7 + 5 + 3 + 1 = 25, which shows that the whole spaces passed through in 5 seconds equal the square of 5.
The momentum, or force, of a body falling through the atmosphere is the mass or weight, multiplied by the square root of the height it has fallen through, multiplied by 8·021.
Suppose a weight of 10 tons to be raised 9 feet, and to drop thence suddenly on a bridge; the momentum is 10 × (3 × 8·021) = 240·63 tons. That is, a weight of 10 tons, so falling, would exert as great a strain to break down the bridge, as the pressure of 240·63 tons of dead weight.
Thus, a one-ounce ball falling from a height of 400 feet, would strike the earth with a momentum of
| oz. feet. | oz. | lb. |
| 1 × (20 × 8·021) | = 160·42 | = 10·026. |
By experiments to ascertain the effect of Carnot’s vertical fire, it was found that 4-oz. balls only penetrated 1 20 of an inch into deal board, and from 2 to 3 inches into meadow ground.
Amplitude signifies the range of a projectile, or the right line upon the ground, subtending the curvilinear path in which it moves.
The time of flight of different shot, and shells is equal to the time a heavy body takes to descend freely from the highest point described by the curve of the projectile.
To find the time of descent:
Divide the given height, or altitude, by 16 1 12 , and the square root of the quotient will be the time required. Thus, if the altitude is 1200 feet, and the time of descent is required,