The task of determining the amount of influence of a single vector in a given direction involves the use of trigonometric functions. The use of these functions to determine the components of a single vector was also discussed in Lesson 1 of this unit. As a quick review, let’s consider the use of SOH CAH TOA to determine the…
Earlier we studied, the method of resolving a vector into its components was thoroughly discussed. During that lesson, it was said that any vector that is directed at an angle to the customary coordinate axis can be considered to have two parts – each part being directed along one of the axes – either horizontally or…
Addition of Forces We studied the use of Newton’s second law and free-body diagrams to determine the net force and acceleration of objects. In that unit, the forces acting upon objects were always directed in one dimension. There may have been both horizontal and vertical forces acting upon objects; yet there were never individual forces…
To illustrate the usefulness of the above equations in making predictions about the motion of a projectile, consider the solution to the following problem. ExampleA pool ball leaves a 0.60-meter high table with an initial horizontal velocity of 2.4 m/s. Predict the time required for the pool ball to fall to the ground and the…
The above equations work well for motion in one-dimension, but a projectile is usually moving in two dimensions – both horizontally and vertically. Since these two components of motion are independent of each other, two distinctly separate sets of equations are needed – one for the projectile’s horizontal motion and one for its vertical motion….
A non-horizontally launched projectile with an initial vertical velocity of 39.2 m/s will reach its peak in 4 seconds. The process of rising to the peak is a vertical motion and is again dependent upon vertical motion parameters (the initial vertical velocity and the vertical acceleration). The height of the projectile at this peak position…
The time for a projectile to rise vertically to its peak (as well as the time to fall from the peak) is dependent upon vertical motion parameters. The process of rising vertically to the peak of a trajectory is a vertical motion and is thus dependent upon the initial vertical velocity and the vertical acceleration (g…
Earlier in this unit, the method of vector resolution was discussed. Vector resolution is the method of taking a single vector at an angle and separating it into two perpendicular parts. The two parts of a vector are known as components and describe the influence of that vector in a single direction. If a projectile is launched…
It has already been stated and thoroughly discussed that the horizontal and vertical motions of a projectile are independent of each other. The horizontal velocity of a projectile does not affect how far (or how fast) a projectile falls vertically. Perpendicular components of motion are independent of each other. Thus, an analysis of the motion of a projectile demands…
The previous diagrams, tables, and discussion pertain to how the horizontal and vertical components of the velocity vector change with time during the course of projectile’s trajectory. Now we will investigate the manner in which the horizontal and vertical components of a projectile’s displacement vary with time.As has already been discussed, the vertical displacement (denoted by the symbol y in the…