![]() ![]() In Newton's mechanical universe, if we know the speeds at which the ball was traveling up and out, the acceleration of the ball's horizontal and vertical speeds due to air resistance (often negligible), and the acceleration in the vertical direction due to gravity, we can predict the flight of the ball. Note that we use the term acceleration to mean any change in velocity: it can be an increase or decrease in speed, or a change in direction, or both a change in speed and direction. The acceleration down causes the ball to slow down in the vertical direction, stop (vertical velocity equals zero), and then fall back to earth with increasing vertical velocity, since the velocity now points along the same direction as the acceleration resulting from gravitational forces. The up and down motion is governed by the law of gravity that says the ball is under constant downward acceleration due to the attractive force between the ball and the earth. The only "outside" force operating on the horizontal motion of the ball is air resistance, and that doesn't slow the ball down much. This speed is governed by the law of inertia that says the ball will continue in its forward motion without change. The ball hits the hand of the waiting fan with close to the same horizontal speed that it started with. But the acceleration due to gravity does affect the upward velocity of the ball, causing it to slow down, stop, and then fall back to earth. ![]() The horizontal component in this case doesn't change, because there is no force operating on that component of the ball's motion. To make it easier to see the effect downward acceleration has on velocity, we break the velocity vector into its vertical (up/down) and horizontal (forward) components. Velocity is represented by the open-headed green arrow. It always points down, with the same magnitude (since gravitational acceleration doesn't change much with small changes in distance from the center of the earth). In this diagram, the force of gravity is represented by the maroon arrow. The size of the arrow indicates magnitude the arrow points in the direction of the vector. In modern motion analysis, we represent vector quantities like force and velocity with arrows. Anyone who has watched a baseball sail out of the the park on a long homerun when the wind is still can tell you that the ball moves straight out toward center field with about the same speed, but rises and falls on the way. We don't actually observe this kind of behavior with projectiles. If we wanted to move an object like an arrow some direction other than down, we had to push it with a force to give it violent motion, and when the source of the force was withdrawn and the force had spent itself, the object would resume its natural motion (usually down toward the center, again). Air, on the other hand, naturally moved away from the center, and fire moved away even more rapidly. ![]() Remember Aristotle's different types of matter? Earth was attracted to "the center", water was also attracted to the center but as strongly. ![]()
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