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A projectile is launched horizontally with a velocity of 40 m/s. After 4 seconds, the magnitude of the horizontal component of velocity is ____ m/s and the magnitude of the vertical component of velocity is ____ m/s.
(Note: Numbers are randomized numbers and likely different from the numbers listed here.)
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The only force on a projectile is the force of gravity. Gravity is a vertical thingand does not affect the horizontal motion. As such, the horizontal acceleration is 0 m/s/s and the horizontal velocity is constant. The horizontal velocity that the projectile had when launched will be the horizontal velocity of the projectile at all times throughout its motion.
The vertical motion of a projectile is independent of the horizontal motion and must be discussed separately. Since there is a vertical force (gravity), there is a vertical acceleration as well. The vertical velocity of a projectile is changing at a rate of about -10 m/s each second (-9.8 m/s each second to be exact). Knowing the acceleration value and the fact that the initial vertical velocity is 0 m/s (see A Very Fine Detail section), one can use a kinematic equation to determine the final vertical velocity after the specified amount of time. See Formula Frenzy section.
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The final velocity of an object after a certain time can be predicted using the kinematic equation:
vf= vo+ a • t
where vf is the final velocity, vo is the initial velocity, a is the acceleration, and t is the time over which the acceleration has occurred.
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The projectile described in this question is "launched horizontally." The significance of these two small words is that the initial vertical velocity is 0 m/s for a horizontally launched projectile. The initial velocity of the such a projectile is entirely horizontal. Thus, the initial velocity is the initial horizontal velocity.
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