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# Pc8 7 motion

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### Pc8 7 motion

1. 1. Motion and Parametric Equations Precalculus 8-7 P. 527
2. 2. Motion <ul><li>Objects that are launched are called projectiles. </li></ul>
3. 3. Motion <ul><li>Objects that are launched are called projectiles. </li></ul><ul><li>The path of a projectile is called its trajectory. </li></ul>
4. 4. Motion <ul><li>Objects that are launched are called projectiles. </li></ul><ul><li>The path of a projectile is called its trajectory. </li></ul><ul><li>The horizontal distance that a projectile travels is its range. </li></ul>
5. 5. Motion <ul><li>Objects that are launched are called projectiles. </li></ul><ul><li>The path of a projectile is called its trajectory. </li></ul><ul><li>The horizontal distance that a projectile travels is its range. </li></ul><ul><li>The motion of a projectile can be described by its position, velocity, and acceleration. </li></ul><ul><ul><li>These can all be represented by vectors. </li></ul></ul>
6. 6. Motion <ul><li>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. </li></ul>
7. 7. Motion <ul><li>Parametric equations can represent the position of the projectile relative to the starting point in terms of the parameter of time. </li></ul>
8. 8. Motion <ul><li>To find the parametric equations, we must write the horizontal and vertical components of the initial velocity. </li></ul>
9. 9. Motion <ul><li>Because gravity does not affect horizontal velocity, it is the magnitude of the horizontal component of the initial velocity </li></ul><ul><ul><li>Therefore, the horizontal position of a projectile after t seconds is </li></ul></ul>
10. 10. Motion <ul><li>Since vertical velocity is affected by gravity, we must adjust the vertical component of initial velocity. </li></ul>
11. 11. Motion <ul><li>Since vertical velocity is affected by gravity, we must adjust the vertical component of initial velocity. </li></ul><ul><li>We can determine the height of the projectile after t seconds by subtracting gravity’s effect from the initial velocity. </li></ul>
12. 12. Gravity <ul><li>The height of an object affected by gravity is </li></ul>
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