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Free Fall & Projectile Motion

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Free Fall Free fall is constant acceleration motion due only to the action of gravity on an object. In free fall, there are no other forces or accelerations acting on an object (including air resistance and other forces of friction).

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Free fall acceleration The magnitude or value of free fall acceleration g = 9.8 m/s 2 (which is approximately 10 m/s 2 ). Use 9.8! The direction of free fall acceleration is always downward so we assign a negative direction to it. Thus, a = −g = −9.8 m/s 2 for free fall near Earth. The magnitude depends on the planet, of course.

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What g does not depend on The magnitude of free fall or gravitational acceleration, g, does not depend on the mass or weight of falling objects. A 1 kg object free falls at the same rate as a 100 kg object! Both at 9.8 m/s 2. “Little gee” (g) does not depend on whether the object is launched upward or sideways.

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Examples of approximate free fall Ball thrown straight upward. Rock dropped straight down. Cannon ball launched sidewise. Satellite in circular orbit. Can you think of other examples? Is a tossed paper airplane in true free fall?

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Is this true free fall?

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Kinematic equations with free fall v f = v i − gΔt Δ d = v i Δt − ½ g(Δt) 2 These are derived by replacing the variable a with −g in the previously discussed kinematic equations.

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Describing downward free fall An object free falling downward from rest increases its velocity at a constant rate (9.8 m/s, 19.6 m/s, 29.4 m/s, …) each second of fall. Using v f = 9.8(Δt) The distance it travels gets larger and larger (4.9 m, 19.6 m, 44.1 m, …) each second. Δd = ½ (9.8)(Δt) 2

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Describing upward free fall “Free fall” technically includes the ascending movement of objects after being launched upwards. An object moving upward (+) after being launched with some initial velocity v i decreases its velocity at a constant rate each second of upward “fall.” At its highest point the instantaneous velocity v f will be 0 m/s.

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Upward “free fall” < At its highest point the instantaneous velocity v f = 0 m/s, but the acceleration a = g is still −9.8 m/s 2. The object is launched upward with some + initial velocity, v i. When it returns to the same location moving downward its displacement d = 0. vivi Velocity and location change each instant but acceleration g does not change! −v i Launched here >

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Constant free fall acceleration At every location during free fall, the acceleration is ALWAYS, ALWAYS −9.8 m/s 2 (near Earth) no matter whether the instantaneous velocity is positive (upward), negative (downward), or zero (at the highest point). That’s why free fall is an example of CONSTANT acceleration!

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Free fall motion diagrams The arrows here represent velocity vectors.

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