When the football travels through the air, it always follows a curved, or parabolic, path because the movement of the ball in the vertical direction is influenced by the force of gravity. As the ball travels up, gravity slows it down until it stops briefly at its peak height; the ball then comes down, and gravity accelerates it until it hits the ground. This is the path of any object that is launched or thrown (football, arrow, ballistic missile) and is called projectile motion.What is the difference between a parabolic path and projectile motion.?Projectile motion is what it sounds like--the motion of a projectile.
If there are no forces on the projectile other than a constant weight (which is a reasonable approximation in many cases), then its path will be a parabola--its horizontal position will be be proportional to time, and its vertical position will be a quadratic function of time, and therefore of horizontal position.
An example of a projectile with a non-parabolic path would be a ballistic missile--once it burns out and clears the atmosphere, it follows an elliptical path until it re-enters.What is the difference between a parabolic path and projectile motion.?Projectile motion is an example of a parabolic path. It can be shown that the vertical position of the football as a function of the football's horizontal position is a quadratic.
In the horizontal direction, the football moves at constant velocity:
x = vcos胃 t
t = x / vcos胃
In the vertical direction, the football undergoes constant acceleration:
y = vsin胃 (t) - 陆g(t)虏
using the result above:
y = vsin胃 (x / vcos胃) - 陆g(x / vcos胃)虏
y = (tan胃) x - (g / 2(vcos胃)虏) x虏
Projectile motion is an example of a parabolic path.What is the difference between a parabolic path and projectile motion.?Parabola is a mathematical curve - an abstract concept. Projectile trajectory is a real curve - traced by a moving object.
Projectiles are said to follow parabolic path as a first approximation to their true motion. Real motions are influenced by air resistance and, if distance is large enough, curvature of the Earth affects the path as well.What is the difference between a parabolic path and projectile motion.?
In a vacuum for point projectiles in an uniform gravitational field, there is no difference.
Edit: The other answers given here are correct. Projectile motion can follow a wide variety of paths, of which the parabola is just a special type. For example, if a rocket is launched above escape velocity from the Earth, it could follow a quite complicated path throughout the solar system if it passes by planets closely enough.
No comments:
Post a Comment