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# Pc8 7 motion

## by vhiggins1 on Jan 12, 2011

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## Pc8 7 motionPresentation Transcript

• Motion and Parametric Equations Precalculus 8-7 P. 527
• Motion
• Objects that are launched are called projectiles.
• Motion
• Objects that are launched are called projectiles.
• The path of a projectile is called its trajectory.
• Motion
• Objects that are launched are called projectiles.
• The path of a projectile is called its trajectory.
• The horizontal distance that a projectile travels is its range.
• Motion
• Objects that are launched are called projectiles.
• The path of a projectile is called its trajectory.
• The horizontal distance that a projectile travels is its range.
• The motion of a projectile can be described by its position, velocity, and acceleration.
• These can all be represented by vectors.
• Motion
• As the projectile moves (over time), gravity will act on the vertical direction. The horizontal component is unaffected by gravity, so (with no air resistance), it remains consistent throughout the trajectory.
• Motion
• Parametric equations can represent the position of the projectile relative to the starting point in terms of the parameter of time.
• Motion
• To find the parametric equations, we must write the horizontal and vertical components of the initial velocity.
• Motion
• Because gravity does not affect horizontal velocity, it is the magnitude of the horizontal component of the initial velocity
• Therefore, the horizontal position of a projectile after t seconds is
• Motion
• Since vertical velocity is affected by gravity, we must adjust the vertical component of initial velocity.
• Motion
• Since vertical velocity is affected by gravity, we must adjust the vertical component of initial velocity.
• We can determine the height of the projectile after t seconds by subtracting gravity’s effect from the initial velocity.
• Gravity
• The height of an object affected by gravity is