Unit 3-2: Trajectories

1. Unit 3-2: Trajectories

2. Projectile Motion • Projectile: Any object moving through the air that is only being affected by gravity • Very similar to freefall • The difference is that it also is moving side to side. • A projectile moves through the air in a curved path called a trajectory.

3. Projectile Motion • Each projectile has a different trajectory based on its launch angle and starting velocity. • Analyzing the trajectories by themselves can be quite confusing, however we break them up into their components to make things easier. • Each trajectory has a horizontal and vertical component.

4. Projectile Motion • When the horizontal and vertical components are brought together, a parabolic trajectory is created. • Observe this next image, note how the distance between the horizontal movement never changes, because velocity is constant. • Observe how the vertical distance changes as time goes on, this is because gravity is accelerating the object.

5. Projectile Motion

6. Projectile Motion • It is very important to remember that gravity only affects objects in the vertical component. • Gravity has absolutely no effect on the horizontal component.

7. Avoiding the dreaded MATH • This section will focus on determining the trajectory of a projectile graphically • It’s a lot faster and easier than any other method.

8. How to draw a trajectory • Start with a vector at an angle • Draw the vector to scale on graph paper • Scale remains: 0.6cm = 10m/s = 1square • Now you determine your Vx. Remember that this remains constant. • Determine your Viy, this will decrease by 10m/s every second that goes by.

9. How to draw a trajectory • Step 2: • Draw, from the end of your first vector, Vx. • Then, from where the Vx ended, draw in Viy, but with one less square. • This is because of gravity acting on it. • Draw in the resultant vector from beginning to end.

10. How to draw a trajectory • Step 3: • Continue drawing Vx and then Vy until the trajectory returns to the ground. • There are some rules for determining range, height and time, but we’ll discuss those shortly. • Ex: Draw the trajectory for 60m/s at 45°

11. The Rules It says here: -To determine time, count all the resultant vectors except the first. -To determine range, count all the Vx vector squares except the first Vx vector. Each square represents 10m. To determine height, count all the Vy vector squares except the first half of the Viy vector

12. Let’s all try some examples! 87m/s at 76° 102m/s at 18° 87m/s at 30°