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Projectile Motion vovo Launch a projectile horizontally from the top of a cliff. Draw the subsequent path of the projectile marking the position of the projectile at equal intervals of time.

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Projectile Motion How much time has passed between subsequent positions? 1 unit of time

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Projectile Motion How much time has passed between subsequent positions? 1 unit of time

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Projectile Motion How much time has passed between subsequent positions? 1 unit of time

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Projectile Motion Draw a pair of horizontal and vertical line from each position. Draw an outline of the projectile at each pair of intersecting lines Draw a horizontal and vertical line extending away from the the projectiles initial position.

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1 unit Describe the horizontal displacements. Projectile Motion How much time passed between subsequent positions? 1 unit of time Whats the displacement between subsequent positions? Horizontal Displacements are EQUAL

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1 unit 5 units 3 units Projectile Motion Describe the vertical displacements. How much time passed between subsequent positions? 1 unit of time Whats the displacement between subsequent positions? xs = Consecutive ODD #s

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Projectile Motion What does each vertical side of a colored region represent? Left Side x Displacement 1 3 5 Consecutive ODD Numbers

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Projectile Motion What does each vertical side of a colored region represent? Right Side Distance Fallen 1 4 9 Square of Consecutive Numbers

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Projectile Motion Whats the relationship between interval displacement and distance fallen? 11 4 3 9 5 Equal 1 +3 4 1 3 +5 9 Distance Fallen = ( x )

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Projectile Motion Describe the motion of the projectile at subsequent positions. Discuss: Velocity and Acceleration

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Projectile Motion Describe the motion of the projectile at subsequent positions. CONSTANT Horizontal Velocity

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Projectile Motion Describe the motion of the projectile at subsequent positions. CHANGING Vertical Velocity

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Projectile Motion Draw an arrow representing the horizontal velocity at each position. vxvx vxvx vxvx vxvx

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Projectile Motion Draw an arrow representing the vertical velocity at each position. vxvx vxvx vxvx vxvx vyvy vyvy vyvy vy=0vy=0

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Projectile Motion Draw an arrow representing the speed at each position. vxvx vxvx vxvx vxvx vyvy vyvy vyvy

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Projectile Motion Use your knowledge of right triangles to draw in the speed. 90

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Projectile Motion Draw an arrow representing the speed at each position. vxvx vxvx vxvx vyvy vyvy vyvy v v v v

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Projectile Motion Use your knowledge of the Pythagorean theorem calculate the speed. 90 v vyvy vxvx v2=vx2+vy2v2=vx2+vy2

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Projectile Motion Draw an arrow representing the acceleration at each position. vxvx vxvx vxvx v=vxv=vx vyvy vyvy vyvy v v v agag agag agag agag But guess what…

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Projectile Motion vxvx vxvx vxvx v=vxv=vx vyvy vyvy vyvy agag agag agag v v v agag

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Kinematics Equations You can still use all these…but just be sure to keep you keep the x and y dimensions separated!

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Projectile Motion You gotta Keep em separated…. Horizontal MotionVertical Motion The X-stuffThe Y stuff

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In a Nut Shell There are TWO IMPORTANT RESULTS: in FREE FALL motion: 1. The distance fallen during EACH INTERVAL increases as the RATIO of ODD INTEGERS. 2. The TOTAL DISTANCE fallen during the entire time interval increases as the ratio of SQUARES

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Projectile Motion Since VELOCITY is relative to the FRAME of REFERENCE, All projectile motion is FREE FALL in the appropriate reference frame. Therefore: The vertical displacements always exhibit: the ratio of squares and ratio of odd integers behavior.

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