1. Projectile Motion Also known as two dimensional motion or trajectory problems

2. Projectile Motion  Projectile motion occurs when objects are launched at an angle so they are moving in both the horizontal and vertical directions

3. Projectile Motion  Key Idea: Because gravity only acts vertically, the way to solve these problems is to separate the problem into a vertical part and a horizontal part and solve them separately.

4. Projectile Motion  Typically the place to start is to resolve the velocity vector (which is at an angle) into a vertical velocity and horizontal velocity.

5. Projectile Motion  Solve the problem by keeping the vertical and horizontal components in separate tables  VerticalHorizontal  The variable which is common to both is time.

6. Projectile Motion  Example: launch a cat at 50m/s at an angle of 30 degrees w/the horizontal  Find the maximum height, horizontal distance, and time in the air  V(horizontal) = 50 x cos(30) = 43.3 m/s  V(vertical) = 50 x sin(30) = 25 m/s

7. Projectile Motion  Vertical  V(vertical) = 25m/s  Time (to peak) = 2.5 seconds so total time up and down is 5.0 seconds  Distance (up) = ½ a t 2 = 31.2m

8. Projectile Motion  Horizontal  We found the total time in the air = 5 seconds (from the vertical part)  The distance travelled horizontally is the horizontal velocity x time = 43.3m/s x 5s = 220m

9. Projectile Motion  Nice visual

10. Projectile Motion  Nicer visual