

Lesson 1: Vectors  Fundamentals and OperationsRelative Velocity and Riverboat Problems
Independence of Perp. Components of
Motion Lesson 2: Projectile MotionCharacteristics of a Projectile's Trajectory Describing Projectiles with Numbers: Horizontal and Vertical Velocity Horiz. Launched Projectiles  Problem Solving
NonHoriz. Launched Projectiles 
Problem Solving Lesson 3 : Forces in Two Dimensions

Lesson 2: Projectile MotionCharacteristics of a Projectile's TrajectoryAs discussed earlier in this lesson, a projectile is an object upon which the only force acting is gravity. Many projectiles not only undergo a vertical motion, but also undergo a horizontal motion. That is, as they move upward or downward they are also moving horizontally. There are the two components of the projectile's motion  horizontal and vertical motion. And since perpendicular components of motion are independent of each other, these two components of motion can (and must) be discussed separately. The goal of this part of the lesson is to discuss the horizontal and vertical components of a projectile's motion; specific attention will be given to the presence/absence of forces, accelerations, and velocity.
Horizontally Launched ProjectilesLet's return to our thought experiment from earlier in this lesson. Consider a cannonball projected horizontally by a cannon from the top of a very high cliff. In the absence of gravity, the cannonball would continue its horizontal motion at a constant velocity. This is consistent with the law of inertia. And furthermore, if merely dropped from rest in the presence of gravity, the cannonball would accelerate downward, gaining speed at a rate of 9.8 m/s every second. This is consistent with our conception of freefalling objects accelerating at a rate known as the acceleration of gravity. If our thought experiment continues and we project the cannonball horizontally in the presence of gravity, then the cannonball would maintain the same horizontal motion as before  a constant horizontal velocity. Furthermore, the force of gravity will act upon the cannonball to cause the same vertical motion as before  a downward acceleration. The cannonball falls the same amount of distance as it did when it was merely dropped from rest (refer to diagram below). However, the presence of gravity does not affect the horizontal motion of the projectile. The force of gravity acts downward and is unable to alter the horizontal motion. There must be a horizontal force to cause a horizontal acceleration. (And we know that there is only a vertical force acting upon projectiles.) The vertical force acts perpendicular to the horizontal motion and will not affect it since perpendicular components of motion are independent of each other. Thus, the projectile travels with a constant horizontal velocity and a downward vertical acceleration.
The above information can be summarized by the following table.
NonHorizontally Launched ProjectilesNow suppose that our cannon is aimed upward and shot at an angle to the horizontal from the same cliff. In the absence of gravity (i.e., supposing that the gravity switch could be turned off) the projectile would again travel along a straightline, inertial path. An object in motion would continue in motion at a constant speed in the same direction if there is no unbalanced force. This is the case for an object moving through space in the absence of gravity. However, if the gravity switch could be turned on such that the cannonball is truly a projectile, then the object would once more freefall below this straightline, inertial path. In fact, the projectile would travel with a parabolic trajectory. The downward force of gravity would act upon the cannonball to cause the same vertical motion as before  a downward acceleration. The cannonball falls the same amount of distance in every second as it did when it was merely dropped from rest (refer to diagram below). Once more, the presence of gravity does not affect the horizontal motion of the projectile. The projectile still moves the same horizontal distance in each second of travel as it did when the gravity switch was turned off. The force of gravity is a vertical force and does not affect horizontal motion; perpendicular components of motion are independent of each other.
In conclusion, projectiles travel with a parabolic trajectory due to the fact that the downward force of gravity accelerates them downward from their otherwise straightline, gravityfree trajectory. This downward force and acceleration results in a downward displacement from the position that the object would be if there were no gravity. The force of gravity does not affect the horizontal component of motion; a projectile maintains a constant horizontal velocity since there are no horizontal forces acting upon it.


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