1. Projectile Motion & Vectors

2. Projectile motion is the motion of an object in flight including the impact of gravity The curved flight of a football or baseball seen during a game is an excellent example of projectile motion

3. Understanding Projectile Motion To understand projectile motion, it is easiest to break the motion down into motion in two directions- x and y We did this last unit with the marble/ramp lab The marble rolling down the ramp at an angle was moving in the x direction (horizontally) and y direction (vertically)

4. Marble/Ramp Vectors Marble rolls down the ramp Marble travels in the x direction Marble travels in the x direction

5. Vectors A vector is a drawing showing direction and magnitude Magnitude is the measure of how large something is Ex. Magnitude 4.5 earthquake, 55 mph A vector sounds a lot like a velocity, and vectors are frequently drawn to represent velocities

6. Drawing vectors A vector is drawn with an arrow pointing the direction of the vector The arrow should be drawn to a scale length Perhaps 1 cm line represents 10m/s

7. Vector examples 45 mph east 9.8 m/s 2 down

8. What good are they? Vectors give a visual representation of the directions of motion Vectors can work together to show us what the net result will look like Vectors can be added to calculate the net result (resultant vector)

9. A Thrown ball The quarterback throws the ball at 9 m/s at a 30° angle (to horizontal) 9 m/s

10. A Thrown ball The ball moves in the x direction 9 m/s The ball moves in the y direction

11. Vectors can add together Vectors can work together to describe the final, or resultant, vector For example A boat traveling down a river gets to go faster because the river “pushes” the boat faster A boat traveling up river goes slower because it has to go against the river

12. River Trip Boat travels 35 mph up river River travels 10 mph downstream Result – boat travels 25 mph up river

13. River Trip Boat travels 35 mph down river River travels 10 mph downstream Result – boat travels 45 mph down river

14. Vectors can add in any direction! Boat travels 35 mph across the river River travels 10 mph downstream Resultant Boat travels 35 mph across the river River travels 10 mph downstream Resultant

15. Calculating the vectors The y vector = sin of angle X velocity sin(30)*9 m/s V y = 4.5 m/s 9 m/s 30° When the football is thrown, it goes upwards at 4.5 m/s

16. Calculating the vectors The x vector = cos of angle X velocity cos(30)*9 m/s V x = 7.79 m/s 9 m/s 30° When the football is thrown, it goes down field at 7.79 m/s

17. Practicing vectors Find the x and y vectors for the football thrown as shown 12 m/s 50° V x = cos(50)*12 m/s V x = 7.71 m/s V y = sin(50)*12 m/s V y = 9.19 m/s

18. Using vectors A projectile has a curved path as it flies It spends half of its flight time on the way up, and half on the way down 12 m/s 50°

19. Using vectors Let’s find how long it takes for the ball to reach the top of its trajectory, or curved path 12 m/s 50°

20. How long does it fly? First, we know it goes up at 9.19 m/s Second, we know velocity at the top of the trajectory is 0 m/s Third, we know that the upwards velocity decreases at 9.8 m/s 2 due to gravity 12 m/s 50°

21. How long does it fly? Use the formula a=(V f -V o )/t -9.8 m/s 2 =(0 m/s-9.19 m/s)/t -9.8 m/s 2 =(-9.19 m/s)/t t=(-9.19 m/s)/(-9.8 m/s 2 ) t=.94 seconds to fly up t total = 2*.94 t total = 1.88 seconds 12 m/s 50°

22. How far it fly? First, we now know the time it flies (1.88 seconds) Second, we know the horizontal velocity (v x ) = 7.71 m/s Use the formula v=d/t 7.71 m/s = d/1.88 seconds d=7.71 m/s * 1.88 s d = 14.49 m 12 m/s 50°

23. Try another (simpler) A marble rolls off a table 1.5 m high with a velocity of 5 m/s How far from the table will it hit the floor? Formulas d=1/2at 2 v=d/t 5 m/s 1.5 m

24. Try another (simpler) Use d=1/2at 2 to find time it drops (and flies away from the table) 1.5 m = ½(9.8 m/s 2 )(t 2 ) 3m/(9.8 m/s 2 )= t 2 t 2 =.31 seconds 2 t =.56 seconds Find the distance 5 m/s=d/.56 seconds 2.8 m = d 5 m/s 1.5 m