8.7 Modeling Motion Using Parametric Equations

1. Assignment #64 You may change the angles to be or 8.7 Modeling Motion Using Parametric Equations By the end of the section students will model motion of a projectile using parametric equations to find the velocity and distance as evidenced by a roundtable activity.

2. By the end of the section students will model motion of a projectile using parametric equations to find the velocity and distance as evidenced by a roundtable activity. Vectors are made of components

3. By the end of the section students will model motion of a projectile using parametric equations to find the velocity and distance as evidenced by a roundtable activity. Because it has magnitude and direction!! The velocity vector Don’t forget velocity is a RATE! • Why the ? • We care about the MAGNITUDE, not the direction. • AND with respect to projectiles they will all be angles in Q1 anyway.

4. By the end of the section students will model motion of a projectile using parametric equations to find the velocity and distance as evidenced by a roundtable activity. Parametric equations for the path of a projectile • If I am traveling at 5 mph, how far did I go in • 1 hour? • 2 hours? • 7 hours? • Distance=rate x time • If I throw a ball in the air, why does it come back down? • GRABity! rate distance time rate time • GRABity!

5. By the end of the section students will model motion of a projectile using parametric equations to find the velocity and distance as evidenced by a roundtable activity. Example 1: Find each of the values using parametric motion equations • Mr. Grau has weak little chicken legs. He kicks a soccer ball with an initial velocity of 8 m/s at an angle of with the ground. • Find the initial vertical velocity. • Find the initial horizontal velocity. • How far has the ball traveled horizontally after 2 seconds • What is the vertical displacement after 2 seconds • At what time does the ball hit the ground? Don’t forget the units!! m/s m/s m m s

6. By the end of the section students will model motion of a projectile using parametric equations to find the velocity and distance as evidenced by a roundtable activity. Example 1: Find each of the values using parametric motion equations Don’t forget the units!! • Ms. Munch has deceptively strong legs and kicks a soccer ball with an initial velocity of 32 m/s at an angle of with the ground. • Find the initial vertical velocity. • Find the initial horizontal velocity. • How far has the ball traveled horizontally after 2 seconds • What is the vertical displacement after 2 seconds • At what time does the ball hit the ground? m/s m/s m m s

7. By the end of the section students will model motion of a projectile using parametric equations to find the velocity and distance as evidenced by a roundtable activity. Example 1: Find each of the values using parametric motion equations Don’t forget the units!! • An arrow is shot with an initial velocity of 16 km/hrand makes a angle with the horizontal. • Find the initial vertical velocity. • Find the initial horizontal velocity. • How far has the ball traveled horizontally after 2 seconds • What is the vertical displacement after 2 seconds m/s m/s s m/s m m

8. By the end of the section students will model motion of a projectile using parametric equations to find the velocity and distance as evidenced by a roundtable activity. Summary • A desk is thrown with an initial velocity of at an angle of with the horizontal. Find the initial vertical and horizontal velocity. • A refrigerator is hit with an initial velocity of ft/s at an angle of with the horizontal. After 2 seconds, how far has the refrigerator travelled horizontally and vertically?

9. By the end of the section students will model motion of a projectile using parametric equations to find the velocity and distance as evidenced by a roundtable activity. Summary • A desk is thrown with an initial velocity of at an angle of with the horizontal. Find the initial vertical and horizontal velocity. • A refrigerator is hit with an initial velocity of ft/s at an angle of with the horizontal. After 2 seconds, how far has the refrigerator travelled horizontally and vertically?

10. By the end of the section students will model motion of a projectile using parametric equations to find the velocity and distance as evidenced by a roundtable activity.

11. By the end of the section students will model motion of a projectile using parametric equations to find the velocity and distance as evidenced by a roundtable activity. Example 1: Find each of the values using parametric motion equations