1. Projectile Motion

2. Consider bodies acted upon by some force… What do they all have? What do they all have? ACCELERATION ACCELERATION Consider direction of applied force or acceleration… In direction of motion  +a In direction of motion  +a Opposite direction of motion  -a Opposite direction of motion  -a At right angles to direction of motion  circular At right angles to direction of motion  circular At right angles to initial direction of motion  parabolic At right angles to initial direction of motion  parabolic F vivi

3. Parabolic Conditions Force at right angles to initial velocity Constant velocity in one direction Ex. Gravity w/ bomb, arrow, bullet Full parabolas  golf ball, football Full parabolas  golf ball, football

4. Consider motion in horizontal & vertical directions Horizontal No additional horizontal forces Object in motion stays in motion v x is constant 1 equation v x = d x /t Vertical -g on way up -g on way down F = ma v f =√2ad+v i 2 D= ½ at 2 + v i t v f =v i + at v y decreases on way up v y increases on way down (in negative direction)

5. Which will hit the ground 1 st ? Bullet dropped or fired? Ball hit off the table with a ruler Ball hit off the table with a ruler Ball hit/dropped at the same time Ball hit/dropped at the same time

6. Plane and bomb to observer on ground To in plane observer – straight down

7. Example Gum wad and Car: Straight Down? Straight Down? Backwards parabola? Backwards parabola? Forward parabola? Forward parabola? Object in motion stays in motion Air friction – slows down Gravity – travels down

8. More Examples… Golf: Hit hard for far and not for close? NOT ALWAYS NOT ALWAYS Angles determine distance Different clubs and swings Arrows Javelin: too large  too much air friction Basketball: only part of parabola

9. Objects fired will drop… An object fired forward will drop. How much? Gun 357 Magnum Muzzle v = 1295 ft/s Muzzle v = 1295 ft/s Distance Velocity Drop 50 yards 1094 ft/s 0.8 inches 100 yards 975 ft/s 3.5 inches

10. To compensate Baseball Throw from above Throw from above Elevate mound Elevate mound Fastball Velocity Mound to Plate Time Drop 85 mi/hr 55 ft.46s 3.3 ft 85 mi/hr 55 ft.46s 3.3 ft 90 mi/hr 55 ft.44s 3 ft 90 mi/hr 55 ft.44s 3 ft

11. Rising Fastball? Not really – rotates at 10,000 rpm Not really – rotates at 10,000 rpm Backspin enough for a 6” rise, therefore it only drops 2.8 or 2.5 feet Backspin enough for a 6” rise, therefore it only drops 2.8 or 2.5 feet If throwing from 3 rd to 1 st – 120 ft at 85 mi/hr If throwing from 3 rd to 1 st – 120 ft at 85 mi/hr If launch at 8° can’t deviate by more than 2° - aim 16 ft over 1 st baseman If launch at 8° can’t deviate by more than 2° - aim 16 ft over 1 st baseman

13. To keep a projectile in the air longer adjust: Velocity (higher) Velocity (higher) Angle (larger) Angle (larger) Largest angle is 90° straight up – in air long but no horizontal distance Greatest height – largest angle and largest velocity Maximum range (d x ) = 45°

14. http://youtube.com/watch?v=Wsq3dWTrR WA http://youtube.com/watch?v=Wsq3dWTrR WA