Projectile motion

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projectile motion

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Next, we consider a particle that moves in a vertical plane during free fall, with its only acceleration being that of the free-fall acceleration g, which is downward. Such a projectile might be a golf ball, a baseball, or any of a variety of other objects. We shall assume that the air has no effect on the motion of the projectile.

Figure 1.10, shows the path followed by a projectile under such ideal conditions. The projectile is launched at some initial velocity , which can be written

Fig. 1.10

The components and then can be found if we know the angle between and the positive x direction:

and

During its two-dimensional motion, the projectile's position vector and velocity vector are changed continuously, but its acceleration vector is constant and alwaysdirected vertically downward. (The projectile has nohorizontal acceleration.) As shown in Fig. 1.11, the angle between the direction of the velocity vector and that of the acceleration vector is not constant but varies during the motion.

Projectile motion, like that in Figs. 1.11 looks complicated, but we have the following simplifying feature (known from experiment): the horizontal motion and the vertical motion are independent on each other.

Fig. 1.11

This feature allows us to break up a problem involving two-dimensional motion into two separate and easier one-dimensional problems, one for the horizontal motion and the other for the vertical motion.

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