Volume 1
A course of lectures on natural philosophy and the mechanical arts / by Thomas Young.
- Thomas Young
- Date:
- 1845
Licence: Public Domain Mark
Credit: A course of lectures on natural philosophy and the mechanical arts / by Thomas Young. Source: Wellcome Collection.
Provider: This material has been provided by King’s College London. The original may be consulted at King’s College London.
64/670 page 30
![The oblique motion of a projectile may be the most easily understood by resolving its velocity into two parts—the one in a horizontal, the other in a vertical direction. It appears from the doctrine of the composition of motion, that the horizontal velocity will not be afiFected by the force of gravitation acting in a direction perpendicular to it, and that it wiU, there- fore, continue uniform ; and that the vertical motion will also be the same as if the body had no horizontal motion. Thus, if we let faU from the head of the mast of a ship a weight which partakes of its progressive motion, the weight will descend by the side of the mast in the same manner and with the same relative velocity as If neither the ship nor the weight had any horizontal motion. We may, therefore, always determine the greatest height to which a pro- jectile will rise, by finding the height from which a body must fall in order to gain a velocity equal to its vertical velocity, or its velocity of ascent; that is, by squaring one eighth of the number of feet that it would rise in the first second if it were not retarded. For example, suppose a musket to be so elevated that the muzzle is higher than the but-end by half of the length, that is, at an angle of 30° ; and let the ball be discharged with a velocity ■ of 1000 feet in a second ; then its vertical velocity wUl be half as great, or 600 feet in a second ; now the square of one eighth of 500 is 3906, conse- quently the height to which the ball would rise, if unresisted by the air, is 3906 feet, or three quarters of a mile. But, in fact, a musket ball actually shot upwards, with a velocity of 1670 feet in a second, which would rise six or seven miles in a vacuum, is so retarded by the air, that it does not j attain the height of a single mile. | We may easily find the time of the body’s ascent from its initial velocity; ■ for the time of ascent is directly proportional to the velocity, and may be found in seconds by dividing the vertical velocity in feet by 32 ; or if we divide by 16 only we shall have the time of ascent and descent; and then the horizontal range may be found, by calculating the distance described in this time with the uniform horizontal velocity. Thus, in the example that we have assumed, dividing 500 by 16 we have 31 seconds for the whole time of the range ; but the hypotenuse of our triangle being 1000, and the perpendicular 500, the base wiU be 886 feet; consequently the hori- i zontal range is 31 times 886, that is, nearly 28,000 feet, or above 5 mUes. ' But the resistance of the air wiU reduce this distance also to less than one - mile. It may be demonstrated that the horizontal range of a body, projected with a given velocity is always proportional to the sine of twice the angle of elevation : that is, to the [sine of the angle of] elevation of the muzzle of the piece in a situation twice as remote from a horizontal position as its actual situation. Hence it follows, that the greatest horizontal range wiU be when the elevation is half a right angle ;* supposing the body to move in a vacuum. But the resistance of the air increases with the length of ) the path, and the same cause also makes the angle of descent much greater i than the angle of ascent, as we may observe in the track of a bomb. For ) both these reasons, the best elevation is somewhat less than 45°, and some- , 1 * Galileo, Dial. IV. Prop. 7, cor.](https://iiif.wellcomecollection.org/image/b21301840_0001_0064.jp2/full/800%2C/0/default.jpg)
