The ball is \(18\,m\) from the base of the cliff when it lands in the sea. The horizontal speed of the ball is constant, so we can use: Optimal angle for a projectile part 3: Horizontal distance as a function of angle (and speed) Optimal angle for a projectile part 4: Finding the optimal angle and distance with a bit of calculus. Optimal angle for a projectile part 2: Hangtime. A projectile is any object that has been thrown, shot, or launched, and ballistics is the study of projectile motion. ![]() Ĭ) The ball travels through the air for \(3s\) before it reaches the sea. Optimal angle for a projectile part 1: Components of initial velocity. So the height of the cliff is \(44.1\,m\). The area under the graph is the vertical distance travelled: Parabolas and ellipses are very close, but as you suspected they will always be approximations.A boy kicks a ball horizontally over the edge of a cliff with a speed of \(6ms^\). Because of these things there is no exact shape that describes such motion, much like there is no shape that exactly describes orbital motion. For projectile motion, you lose accuracy because the earth is not a perfect sphere with uniform gravitation, there's no such thing as a perfect vacuum, etc etc etc. Projectile motion is a form of motion experienced by an object or particle (a projectile) that is projected in a gravitational field, such as from Earths surface, and moves along a curved path under the action of gravity only. Paraphrasing a quote often attributed to the statistician George Box "all models are wrong, some are useful". But no matter what, the model will never exactly explain what is going on because reality never exactly matches the assumptions of a model. It's a much different story if you throw a light big object during a windy day. In the case of projectile motion, the standard equations work quite well if you throw a small dense object inside a windless room. How good your explanation/predictions are depends on 1)how good the model is and 2)how close your situation is to the assumptions made by the model. The crucial concept is that vertical acceleration does not affect horizontal velocity. It concerns objects accelerating vertically when projected horizontally or vertically. (This is an informal definition.) The path of a projectile is called its trajectory. This episode looks at the independence of vertical and horizontal motion. Models employ simplifying assumptions in order to make problems tractable so we can explain what is happening and hopefully make predictions. A projectile is any object that is cast, fired, flung, heaved, hurled, pitched, tossed, or thrown. ![]() And by definition, a model is an imperfect representation of reality. It is an approximation, as everything in physics is an approximation based on mathematical/statistical modeling. Other answers can be found in these "duplicate" posts: Elliptical Trajectory, or Parabolic? and Why does the Earth follow an elliptical trajectory rather than a parabolic one? Can a very small portion of an ellipse be a parabola?Įdit: yes, in a spatially constant and uniform gravitational field, a parabola is exact. Why do you have parabolas in the "simple" setting you are describing? Because you can always approximate locally an ellipse with a parabola. However, the Earth is not a point and has a finite radius: some of those ellipses (starting at the Earth surface) will intersect at later times the Earth surface again. ![]() Leave out open orbits, which means that you are shooting the projectile at infinity. Now, you may know that a test particle in this $1/r^2$ force field of the Earth can have different orbits (closed or open, depending on the initial velocity and the initial position). The gravitational field of the Earth is the same as the one produced by a point particle in its center (with the same mass, the usual $1/r^2$ gravitational force field). Analyzing the whole complicated motion as a superposition of manageable parts is a paradigm of modern theoretical physics. Assume Galilean relativity and Newtonian gravity.
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