To say that a projectile has a vertical acceleration of -9.8 m/s/s is to say that the vertical velocity changes by 9.8 m/s (in the - or downward direction) each second. An acceleration value indicates the amount of velocity change in a given interval of time. When first introduced, it was said that acceleration is the rate at which the velocity of an object changes. The process of determining the time to rise to the peak is an easy process - provided that you have a solid grasp of the concept of acceleration. 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 = 9.8 m/s/s, down). 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. We will begin with the determination of the time. This process is demonstrated on the remainder of this page. Then click the Submit button to check your answers.Īs mentioned above, the point of resolving an initial velocity vector into its two components is to use the values of these two components to analyze a projectile's motion and determine such parameters as the horizontal displacement, the vertical displacement, the final vertical velocity, the time to reach the peak of the trajectory, the time to fall to the ground, etc. Use your calculator to determine the values of v x and v y. Enter any velocity magnitude and angle with the horizontal. Need more practice? Use the Velocity Components for a Projectile widget below to try some additional problems. (If necessary, review this method on an earlier page in this unit.) The sketch is shown at the right and the use of trigonometric functions to determine the magnitudes is shown below. These numerical values were determined by constructing a sketch of the velocity vector with the given direction and then using trigonometric functions to determine the sides of the velocity triangle. These are known as the horizontal and vertical components of the initial velocity. Such a projectile begins its motion with a horizontal velocity of 25 m/s and a vertical velocity of 43 m/s. Thus, the analysis of projectile motion problems begins by using the trigonometric methods discussed earlier to determine the horizontal and vertical components of the initial velocity.Ĭonsider a projectile launched with an initial velocity of 50 m/s at an angle of 60 degrees above the horizontal. The vertical velocity component ( v y) describes the influence of the velocity in displacing the projectile vertically. The horizontal velocity component ( v x) describes the influence of the velocity in displacing the projectile horizontally. If a projectile is launched at an angle to the horizontal, then the initial velocity of the projectile has both a horizontal and a vertical component. The two parts of a vector are known as components and describe the influence of that vector in a single direction. Vector resolution is the method of taking a single vector at an angle and separating it into two perpendicular parts. It is for this reason that one of the initial steps of a projectile motion problem is to determine the components of the initial velocity.ĭetermining the Components of a Velocity VectorĮarlier in this unit, the method of vector resolution was discussed. That is, if analyzing the motion to determine the vertical displacement, one would use kinematic equations with vertical motion parameters (initial vertical velocity, final vertical velocity, vertical acceleration) and not horizontal motion parameters (initial horizontal velocity, final horizontal velocity, horizontal acceleration). Thus, an analysis of the motion of a projectile demands that the two components of motion are analyzed independent of each other, being careful not to mix horizontal motion information with vertical motion information. Perpendicular components of motion are independent of each other. The horizontal velocity of a projectile does not affect how far (or how fast) a projectile falls vertically. It has already been stated and thoroughly discussed that the horizontal and vertical motions of a projectile are independent of each other.
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