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HORIZONTALLY LAUNCHED PROJECTILE MOTION EQUATIONS VERTICAL MOTION OBJECT FROM REST (Vi = 0)

HORIZONTALLY LAUNCHED PROJECTILE MOTION EQUATIONS VERTICAL MOTION OBJECT FROM REST (Vi = 0) V fy = -g D t Velocity final in y-direction (given time) V fy = √-2g D y Velocity final in y-direction (given distance)

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HORIZONTALLY LAUNCHED PROJECTILE MOTION EQUATIONS VERTICAL MOTION OBJECT FROM REST (Vi = 0)

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  1. HORIZONTALLY LAUNCHED PROJECTILE MOTION EQUATIONS VERTICAL MOTION OBJECT FROM REST (Vi = 0) Vfy = -gDt Velocity final in y-direction (given time) Vfy = √-2gDy Velocity final in y-direction (given distance) Dy = -1/2(gDt2) Distance in y-direction or height (given time) ALSO Dt = √(-2Dy)/g Time at given height (some problems may use “h” in place of “Dy”) HORIZONTAL MOTION Vx = constant Vx = Dx/ Dt Dx = Vx Dt Distance in x-direction or range (given time) solving for Dt in one dimension gives Dt in the other dimension HORIZONTALLY LAUNCHED PROJECTILE MOTION EQUATIONS VERTICAL MOTION OBJECT WITH INITIAL VELOCITY (Vi ≠0) Vfy = Viy -(gDt) Vfy = √ Viy2-(2gDy) Dy = ViyDt -1/2(gDt2)

  2. HORIZONTALLY LAUNCHED PROJECTILE MOTION EQUATIONS MAGNITUDE OF RESULTANT VELOCITY CAN BE FOUND USING THE PYTHAGOREAN THEOREM

  3. HORIZONTALLY LAUNCHED PROJECTILES EXAMPLE PROBLEM: SOLVING FOR A HORIZONTALLY LAUNCHED OBJECT P157 Glencoe, 2002 A stone is thrown horizontally at 15m/s from the top of a cliff 44m high. • How far from the base of the cliff does the stone hit the ground? • How fast is it moving the instant it hits the ground? DIAGRAM GIVEN UNKNOWN EQUATION SOLVING FOR Dx SUBS/SOLVE Dx SOLVE Dt SOLVE Vfy

  4. HORIZONTALLY LAUNCHED PROJECTILES EXAMPLE PROBLEM: SOLVING FOR A HORIZONTALLY LAUNCHED OBJECT P157 Glencoe, 2002 A stone is thrown horizontally at 15m/s from the top of a cliff 44m high. • How far from the base of the cliff does the stone hit the ground? • How fast is it moving the instant it hits the ground? GIVEN Vx and Vy SOLVE V

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