2.4 Motion in Two Dimensions

1. 2.4 Motion in Two Dimensions

2. SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. • f. Measure and calculate two-dimensional motion (projectile and circular) by using component vectors. Standard

3. Projectile -Any object which projected by some means and continues to move due to its own inertia (mass). Motion is affected by gravity. It is a projectile from the moment it is launched until the instant before it hits the ground 2.4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

4. Projectiles Move in Two Dimensions Since a projectile moves in 2-dimensions, it therefore has 2 components just like a resultant vector. Horizontal and Vertical

5. Acceleration is caused by gravity In what axis? Only in the y What happens in the x? Constant velocity 2.4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

6. So if there is no gravity 2.4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

7. The actual pathway has constant x velocity and changing y Acceleration in the -y 2.4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

8. Horizontal Velocity Component • NEVER changes, covers equal displacements in equal time periods. • This means the initial horizontal velocity equals the final horizontal velocity • In other words, the horizontal velocity is CONSTANT. BUT WHY? • Gravity DOES NOT work horizontally to increase or decrease the velocity.

9. In the y axis, acceleration is always -9.80m/s2 All the acceleration equations apply In the y axis motion is identical to falling dy = vi y t+ ½ at2 v f y= vi y + at vf y2= vi y2 + 2ad 2.4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

10. Vertical Velocity Component Changes (due to gravity), does NOT cover equal displacements in equal time periods.

11. Combining the Components Together, these components produce what is called a trajectory or path. This path is parabolic in nature.

12. Projectile Motion: Basic Equations Measure and calculate two-dimensional motion by using component vectors.

13. We will assume no air resistance gravity is -9.80 m/s2 the Earth is not moving (Frame of Reference) That leaves the following variables 2.5 Projectile Motion: Basic Equations Measure and calculate two-dimensional motion by using component vectors.

14. The two axes are independent of each other except for time 2.5 Projectile Motion: Basic Equations Measure and calculate two-dimensional motion by using component vectors.

15. 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

16. Projectiles which have NO upward trajectory and NO initial VERTICAL velocity. 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

17. If an object is launched at 0o So our chart becomes 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

18. Now we can fill in whatever else is given in the problem 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

19. Horizontally Launched Projectiles To analyze a projectile in 2 dimensions we need 2 equations. One for the x direction and one for the y direction. And for this we use 2 kinematic equation Horizontal = v x = dx/t Vertical = dy= ½ at2

20. A person on a skate board with a constant speed of 1.3 m/s releases a ball from a height of 1.25 m above the ground. What variable can you fill in? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

21. A person on a skate board with a constant speed of 1.3 m/s releases a ball from a height of 1.25 m above the ground. What variable can you fill in? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

22. We are now prepared to answer some questions A) How long is the ball in the air? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

23. We are no prepared to answer some questions A) How long is the ball in the air? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

24. Basically a one dimensional problem Notice that time is the same in both the Y and the X 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

25. We can now solve for X variable if we want B) What is the x displacement? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

26. We can now solve for distance in the x direction if we want B) What is the x displacement? 2.6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

27. Example A plane traveling with a horizontal velocity of 100 m/s is 500 m above the ground. At some point the pilot decides to drop some supplies to designated target below. (a) How long is the drop in the air? (b) How far away from point where it was launched will it land?

28. Example Then: vx = dx/t 100 = dx/10.1 dx = 1010 m • A plane traveling with a horizontal velocity of 100 m/s is 500 m above the ground. At some point the pilot decides to drop some supplies to designated target below. • (a) How long is the drop in the air? • (b) How far away from point where it was launched will it land? • dy = ½ at2 • -500 = ½ (-9.8)t2 • t = 10.1 s

29. 2.7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

30. Vertical Launch Angle