1. 4 OPO’s / MP’s IN PROJECTING 1. maximum Horizontal distance (D horiz ) 2. maximum Vertical distance (D vert ) 3. maximum Accuracy 4. maximum Accuracy with Speed

2. Projection Angle (  res ) V horiz V vert   res less than 45º  long throw  long jump  Figure 12.1 page 388   res of 20° = V horiz almost 3 times greater than V vert   res greater than 45º  volleyball jumps  high jump  Figure 12.1 page 388   res of 60° = V vert more than 2 times greater than V horiz

3. Vector Composition  Find Resultant e.g. Resultant Velocity (V res )  Pythagorean Theorem  Resultant² which is unknown = the sum of the squares of other 2 components which are known  V res² = V horz² + V vert²  V res² = 4² + 3² V res = 5 mps @ x°

4. FORCES Affecting Projectiles I. GRAVITY directed toward center of earth @ 9.8m/sec² directed toward center of earth @ 9.8m/sec² decelerates on ascent, accelerates on descent decelerates on ascent, accelerates on descent II. DRAG results from airflow past projectile results from airflow past projectile comprised of: comprised of: 1. Profile/Form drag 2. Skin Friction/Surface drag

5. PROFILE/FORM DRAG Primary factor influencing magnitude of drag Primary factor influencing magnitude of drag magnitude is proportional to the size/area of leading edge of projectile (larger size = more drag) magnitude is proportional to the size/area of leading edge of projectile (larger size = more drag) higher pressure zone on leading side and a lower pressure zone on trailing side of projectile higher pressure zone on leading side and a lower pressure zone on trailing side of projectile suction on trailing side suction on trailing side reduced by streamlining reduced by streamlining

6. SKIN FRICTION/SURFACE DRAG  Secondary factor influencing magnitude of drag  Boundary layer of air “sticks” to projectile  rougher surfaces create more friction (“sticking”)  reduced using smooth surfaces, tight fitting wear

7. Projecting for maximum V vertical g is resistive then motive g is resistive then motive F drag is always resistive in aerodynamics F drag is always resistive in aerodynamics greater V of projectile = greater F drag greater V of projectile = greater F drag on descent, acceleration influenced by F drag on descent, acceleration influenced by F drag greater projection V = greater height achieved greater projection V = greater height achieved

8. V vertical 1. Height of C of G at takeoff point (higher CG @ takeoff = higher apex in flight) 2. V vert of C of G at takeoff (greater = higher) 3. Location of reaching fingertips @ apex see Figure 12.4 on page 392

9. Vertical Projection with some V horiz  Tumbling - flip-flops increase ground reaction F  High Jump - carry body from takeoff to pit  Women’s WR 2m09 / 1m78 tall [diff. 31cm] Milt Ottey 2m32 / 1m77 tall [diff. 55cm]  Straddle vs Flop Figures 12.5, 12.6 on page 394  Pole Vault - V horz critical for pole rotation

10. V horizontal  More common in sports  F resistive are g, air resistance, ground friction  Critical Features for max. V horiz projections are: 1. v of release [faster = farther] most important 2. ht of release [higher = farther] 3.  of release [see FIG 12.8 on page 397]  see FIG 12.9 on page 399

11. Factors Affecting D HORZ of Projectiles

12. “Basic Biomechanics” by Susan J. Hall page 345

13. Vertical Target Horizontal Target  darts, archery  FIG 12.15 on page 406  farther target requires more V vert projection  basketball, golf, shoes  BB rim diameter:   =  margin of error  FIG 12.16 on page 408  best BB shooters have greater shld flexion + more elbow extension at release