“I should have thought the very reverse,” cried Louisa, “and that it would have fallen quicker than it rose.”
“You have forgotten to take into account the force with which the stone is projected upwards, and which is destroyed by gravity before it begins to descend.”
“Certainly,” answered Louisa; “but the force 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, while the force given to the stone is entirely optional. I may throw it up gently or otherwise, as I please.”
“If you throw it gently,” said her father, “it will not rise high, and gravity will soon bring it down again; if you throw it with violence, it will rise much higher, and gravity will be longer in bringing it back again to the ground. Suppose, for instance, that you throw it with a force that will make it rise only sixteen feet; in that case, you know, 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 of time; here, then, the times of 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 it is the greater or less distance to which the body rises that makes these two forces balance each other.”
“Thank you, dear papa, for the pains you have taken in explaining this subject to us.”
“Nay,” replied Mr. Seymour, “bestow your thanks upon those to whom they are more justly due; Mrs. Marcet is entitled to the merit of this explanation; for I obtained it from her ‘Conversations.’ Before I quit this subject, I would just observe that, when we come to the consideration of the bow and arrow, you will, by the application of the law I have endeavoured to expound, be enabled to ascertain the height to which your arrow may ascend, with the same facility as you discovered the depth of the well: for, since the times of ascent and descent are equal, you have only to determine the number of seconds which intervene between the instant at which the arrow quits the bow to that at which it falls to the ground, and halving them, to make the usual calculation.--But let us proceed to another subject. Roll the ball hither, Tom; roll the ball hither, I say! you stand as if you thought it would advance to us of its own accord.”
“I know a little better than that, too,” cried Tom; “no body can move without the application of some force.”
“Nor stop, either,” added Mr. Seymour, “when it is once in motion; for matter is equally indifferent to both rest and motion.”
“And yet, papa,” cried Louisa, “unfortunately for your assertion, the ball stopped just now, and I am sure that no force was used to make it do so.”
“And pray, Miss Pert, why are you so sure that no force was opposed to its progress? I begin to fear that my lesson has been thrown away upon you, or you would not, surely, have concluded so falsely.”