1. Projectile motion diagram Questions concerning previous slide What is the point of this picture? vx & vy are independent Determining muzzle velocity Determining final velocity

2. Questions concerning previous slide 1)What does each of the following designate? v ox, v x, v oy, v y, d x, d y, v? Say it in words.v oxv xv oyv yd xd yv 2)Why does v x = v ox ?v x = v ox 3)What is the value of v oy ?value of v oy 4)What is the value of v y ?value of v y 5)What is the value of v ox & v x ?value of v ox & v x ? 6)What is the value of v?value of v Diagram

3. v ox ·v ox = the initial velocity in the horizontal direction. · v ox = muzzle velocity of, in this case, the cannon

4. VxVx ·v x is the final velocity in the horizontal direction or the velocity @ any point in time in the horizontal direction.

5. v oy ·V oy is the initial velocity of the projectile in the vertical direction.

6. vyvy ·v y is the final velocity in the vertical direction or the velocity in the vertical direction @ any point in time.

7. dxdx d x is the distance traveled by the projectile in the horizontal direction. Also called “range” & sometimes designated “R”.

8. dydy ·d y is the heighth from which the projectile is fired or the vertical distance the projectile falls.

9. v ·v = the final velocity of the projectile just before it strikes the ground or the velocity of the projectile @ any point in time. That is, polar form of the vector w/ vx & vy being the rectangular form.

10. v x = v ox ·v x = v ox b/c there is no acceleration in the horizontal direction if we neglect air resistance (which is negligible with a cannonball or for any projectile over short vertical falls).

11. Value of v oy ·v oy = 0 since the cannonball was projected horizontally.

12. Values Value of v y ·v y = v oy 2 + 2gd y · Do you understand how we arrived @ this? Value of v ox & v x v x = v ox = d x /t x

13. Value of v ·v = v x + v y · i.e. the vector sum ·v x & v y = rectangular form ·v = polar form

14. What is the point of this picture? ·Also se fig. 6-1 p. 148 of your text, essentially the same picture. ·This picture depicts a device that shoots & drops 2 balls simultaneously. ·Projectile motion diagramProjectile motion diagram

15. v x & v y are independent ·The velocity in the vertical direction is unaffected by what is happening in the horizontal direction. Return to the previous slide & notice that the vertical posn. of the projected ball & dropped ball is always the same! ·Projectile motion diagramProjectile motion diagram Last slide

16. v x & v y ·Velocity in the horizontal direction is constant. ·Velocity in the vertical direction is inconstant, vy ≠ voy. Velocity in the vertical direction varies in accordance w/ g & time.

17. Determining muzzle velocity Muzzle velocity is the velocity w/ which a bullet emerges from the barrel of a gun. ·v ox = v x ·& v x = d x /t x ·Therefore, we must know d x & t x ·d x can be measured. Projectile motion diagram

18. Determining muzzle velocity - cont. 5)& t x = t y How fast something falls is independent of v o. This is true as long as v o is totally in the x direction i.e. v oy = 0. Projectile motion diagram

19. It may appear to be affected less when moving @ faster speeds but this is only b/c of the v x /v y ratio 1)Since t x = t y 2)t y = ? 3)d y = v oy t + 1/2 gt y 2 4)t y = 2d y /g 5)Not we can calculate v x. v x = d x /t x Projectile motion diagram

20. Determining final velocity ·v = v x + v y ·v x - calculated on previous slides ·v y can be calculated (instant before it hits the ground). ·v y 2 = v oy 2 + 2gd y ·v y = 2gd y ·Projectile motion diagramProjectile motion diagram

21. Determining final velocity - cont. ·tan  = v y /v x ·Magnitude: · cos  = v x /v or sin  v y /v ·v = v x /cos  or v = v y /sin  ·Better yet since we know v x & v y Simply R->P ·Projectile motion diagramProjectile motion diagram

22. Air resistance ·So far air resistance has not been considered. ·There are 2 ways air resistance affects projectile motion. 1)Decrease v x 2)Decrease v y Think about it!

23. Ballisitics ·The study of projectile motion which considers all forces working on a projectile -- that is, it considers air resistance as well as gravity.

24. Key concept ·The velocity in the vertical direction is unaffected by what is happening in the horizontal direction.