Emily. If you throw a stone perpendicularly upwards, is it not the same length of time in ascending, that it is in descending?
Mrs. B. Exactly; in ascending, the velocity is diminished by the force of gravity; in descending, it is accelerated by it.
Caroline. I should then imagine that it would fall, quicker than it rose?
Mrs. B. You must recollect that the force with which it is projected, must be taken into the account; and that this force is overcome and destroyed by gravity, before the body begins to fall.
Caroline. But the force of projection given to a stone in throwing it upwards, cannot always be equal to the force of gravity in bringing it down again; for the force of gravity is always the same, whilst the degree of impulse given to the stone is optional; I may throw it up gently, or with violence.
Mrs. B. If you throw it gently, it will not rise high; perhaps only sixteen feet, in which case it will fall in one second of time. Now it is proved by experiment, that an impulse requisite to project a body sixteen feet upwards, will make it ascend that height in one second; here then the times of the ascent and descent are equal. But supposing it be required to throw a stone twice that height, the force must be proportionally greater.
You see then, that the impulse of projection in throwing a body upwards, is always equal to the action of the force of gravity during its descent; and that whether the body rises to a greater or less distance, these two forces balance each other.
I must now explain to you what is meant by the momentum of bodies. It is the force, or power, with which a body in motion, strikes against another body. The momentum of a body is the product of its quantity of matter, multiplied by its quantity of motion; in other words, its weight multiplied by its velocity.
Caroline. The quicker a body moves, the greater, no doubt, must be the force which it would strike against another body.
Emily. Therefore a light body may have a greater momentum than a heavier one, provided its velocity be sufficiently increased; for instance, the momentum of an arrow shot from a bow, must be greater than that of a stone thrown by the hand.