When a projectile is released with a non-zero horizontal velocity, its trajectory takes on the shape of a parabola. There are now two dimensions to its motion:
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Vertically, gravity is still accelerating it at -9.8 m/sec2.
- Horizontally, there is no acceleration since gravity acts at right angles to that velocity's component.
Consequently, the trajectory must be analyzed in two parts.
Horizontally, the projectile travels at a constant velocity. Gravity acts perpendicularly to the projectile's horizontal component and therefore does not produce any linear acceleration. In the following diagram, the fact that the horizontal velocity remains constant is indicated by the equally spaced dots across the top. Vertically, the projectile is accelerating towards the center of the earth at the rate of 9.8 m/sec2. This uniform acceleration is indicated by the fact that the vertical dots have an ever-increasing separation. As a direct consequence of the equation s = vot + ½ at2, the vertical spacing between dots increases by odd integers.
When a projectile is released completely horizontally, then we start with the following conditions:
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Horizontal motion
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Vertical motion
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time
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| a = 0 |
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a = - 9.8 m/sec2 |
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v = vH |
vo = 0
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R = vHt
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s = vot + ½at2 |
In this table, the variable, R, represents the range of the projectile, or the horizontal distance that the projectile travels from the point of release until it strikes the ground. Note that the time, crosses between the components. That is, time is a parameter that applies to both columns - a common quantity. |