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### Projectile motion

1. 1. PROJECTILE MOTION 1/21/2014 IB Physics (IC NL) 1
2. 2. Projectile Motion Motion in Two Dimension 1/21/2014 IB Physics (IC NL) 2
3. 3. Topic objectives      State the independence of the vertical and the horizontal components of velocity for a projectile in a uniform field. Describe and sketch the trajectory of projectile motion as parabolic in the absence of air resistance. Describe qualitatively the effect of air resistance on the trajectory of a projectile. Solve problems on projectile motion. Remarks: 1. Proof of the parabolic nature of the trajectory is not required. 2. Problems may involve projectiles launched horizontally or at any angle above or below the horizontal. Applying conservation of energy may provide a simpler solution to some problems than using projectile motion kinematics equations. 1/21/2014 IB Physics (IC NL) 3
4. 4. What is a projectile?    1/21/2014 When a body is in free motion, (moving through the air without any forces apart from gravity and air resistance), it is called a projectile Normally air resistance is ignored so the only force acting on the object is the force due to gravity This is a uniform force acting downwards IB Physics (IC NL) 4
5. 5. Types of projectiles There are three types of projectile depending on the value of the angle between the initial velocity and the x-axis. 1. θ = 0 horizontal projectile 2. θ = 90 vertical projectile (studied earlier) 3. θ = θ which is the general case. 1/21/2014 IB Physics (IC NL) 5
6. 6. HORIZONTAL PROJECTILES •Horizontal Projectiles are easiest to work with •only formula used in horizontal (x) direction is: x = ut Remark: in case of horizontal projectiles select the direction of the y-axis to be downward. 1/21/2014 IB Physics (IC NL) 6
7. 7. HORIZONTAL PROJECTILES •Horizontal Projectiles are the most basic •only formula used in horizontal (x) direction is: x = ut constant speed! 1/21/2014 IB Physics (IC NL) 7
8. 8. HORIZONTAL PROJECTILES •vertical (y) direction is just freefall •all of the initial velocity is in the x direction •So, u t1 t2 t3 t4 1/21/2014 IB Physics (IC NL) 8
9. 9. EXAMPLE A person decides to fire a rifle horizontally at a bull’s-eye. The speed of the bullet as it leaves the barrel of the gun is 890 m.s-1. He’s new to the ideas of projectile motion so doesn’t aim high and the bullet strikes the target 1.7 cm below the center of the bull’s-eye. What is the horizontal distance between the rifle and the bull’s-eye? start by drawing a picture: label the explicit givens 890 m.s 1 1.7 cm 1/21/2014 IB Physics (IC NL) 9
10. 10. EXAMPLE What is the horizontal distance between the rifle and the bull’s-eye? X ux 890 m.s Y 1 y ay uy 1.7 cm m 9.8 2 s 1 0 m.s 890 m.s 1m 100cm 0.017m 1 1.7 cm want: 1/21/2014 dx horizontal distance IB Physics (IC NL) 10
11. 11. EXAMPLE which equation do we use? use y 0 1 2 ayt uyt 2 to find time rewrite equation for t t 1/21/2014 2y ay 2(0.017) 9.8 IB Physics (IC NL) 0.059 s 11
12. 12. EXAMPLE Use t and ux to solve for x x 1/21/2014 uxt (890)(0.059) IB Physics (IC NL) 52.4 m 12
13. 13. 1/21/2014 IB Physics (IC NL) 13
14. 14. NON-HORIZONTAL PROJECTILES • vx = ux is still constant • uy is also constant •only difference with non-horizontal is that vy is a function of time u 1/21/2014 IB Physics (IC NL) 14
15. 15. NON-HORIZONTAL PROJECTILES •Angled Projectiles require a little work to get useful u •u has an x and y component •need to calculate initial ux and uy u 1/21/2014 IB Physics (IC NL) 15
16. 16. NON-HORIZONTAL PROJECTILES •need to calculate initial u y usin ux and uy v ux 1/21/2014 IB Physics (IC NL) u cos 16
17. 17. VISUALIZING PROJECTILES •first enter vectors •focus on ux vx = ux is constant the whole flight! 1/21/2014 IB Physics (IC NL) 17
18. 18. VISUALIZING PROJECTILES •first enter vectors •focus on vx •focus on vy no vy at the top! vy decreases as it rises! by how much per second? 1/21/2014 IB Physics (IC NL) 18
19. 19. VISUALIZING PROJECTILES 1/21/2014 IB Physics (IC NL) 19
20. 20. Boundary conditions: at t = 0, x0 = y0 = 0 ux = ucosθ and uy = usinθ 1/21/2014 IB Physics (IC NL) 20
21. 21. Mathematical analysis  1/21/2014 IB Physics (IC NL) 21
22. 22. Importance of time Whatever you need to calculate look for time which is common for x and y  1/21/2014 IB Physics (IC NL) 22
23. 23. LET’S 1/21/2014 ANALYZE THE JUMP IB Physics (IC NL) 23
24. 24. VARIED ANGLES •which projectile angle shoots highest? •larger θ means faster uy •which projectile angle shoots farthest? •45° has perfect balance of fast vx and long flight time. 1/21/2014 IB Physics (IC NL) 24
25. 25. If projectiles are launched at the same speed, but at different angles, the height and range is of the projectile are affected. 1/21/2014 IB Physics (IC NL) 25
26. 26. Solving Problems Involving Projectile Motion 1. Read the problem carefully, and choose the object(s) you are going to analyze. 2. Draw a diagram. 3. Choose an origin and a coordinate system. 4. Decide on the time interval; this is the same in both directions, and includes only the time the object is moving with constant acceleration g. 5.Examine the x and y motions separately.
27. 27. Solving Problems Involving Projectile Motion (cont.) 6. List known and unknown quantities. Remember that vx never changes, and that vy = 0 at the highest point. 7. Plan how you will proceed. Use the appropriate equations; you may have to combine some of them. 1/21/2014 IB Physics (IC NL) 28
28. 28. When the effect of air resistance is significant, the range of a projectile is diminished and the path is not a true parabola. 22
29. 29. In the case of air resistance, the path of a high-speed projectile falls below the idealized path and follows the solid curve. Computer-generated trajectories of a baseball with and without drag. 23
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