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Projectiles Chapter 5

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If we ignore the effects of air resistance an object in the air has a horizontal acceleration of ax = 0 m/s 2 and a vertical acceleration of ay = −9.8 m/s 2. Since ax = 0 the horizontal velocity is constant throughout the flight. The vertical acceleration of −9.8 m/s 2 causes the vertical velocity to decrease on the way up, be 0 at the peak of the flight and increase in the negative direction on the way down.

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Explanation of the Variables for Projectile Motion a = −9.8 m/s 2 a is vertical acceleration Vyi Initial Vertical Velocity Vyf Final Vertical Velocity yi Initial Height yf Final Height t Time x Horizontal Distance If we assume air resistance is negligible, then Ax horizontal acceleration is zero.

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Vertical Motion Equations Horizontal Motion Equation

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Vertical Motion Equations Use to solve for time between velocity points. Use to solve for initial or final velocity when given time.

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Vertical Motion Equations Use to find any of the following variables Vy i Initial Vertical Velocity Vy f Final Vertical Velocity y i Initial Height y f Final Height

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Vertical Motion Equations This equation is used to find the height at some time point.

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This equation can be used to find: The horizontal distance traveled in some time interval. The time to travel a horizontal distance. The horizontal velocity needed to travel a distance in a given time interval. Horizontal Motion Equation

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Takeoff and landing height effects the time to the peak and the time down.

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A ball is kicked with an initial vertical velocity (Vyi) of 14 m/s, find the vertical velocity of the ball after 2.4 seconds.

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A football is punted with an initial vertical velocity (Vy i ) of 18 m/s, find the time to the peak.

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A golf ball lands with a final vertical velocity (Vy f ) of −23 m/s, find the time down (peak to landing).

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A javelin is thrown with an initial height (y i ) of 1.3 m, initial vertical velocity (Vy i ) of 18 m/s, find the peak height (y f ).

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A baseball lands with a final height (y f ) of 0 m, final vertical velocity (Vy f ) of −37 m/s, find the peak height (y i ).

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A pole vaulter falls from peak height (y i ) of 4.1 m to a final height (y f ) of 1.1 m, find the final vertical velocity (Vy f ) of the pole vaulter.

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A golf ball is hit with an initial height (y i ) of 1.8 m, initial vertical velocity (Vy i ) of 23 m/s, a horizontal velocity (Vx) of 32 m/s find the height (y f ) of the ball after 3.6 seconds. Compute the horizontal distance (x) the ball covers during the 3.6 seconds.

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