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ESS 303 – Biomechanics

ESS 303 – Biomechanics. Projectiles. Which Will Hit First?. Y = 1/2 at 2. Put Things Together (4 Steps). Step #1: Calculate the X and Y components of movement. V X0 = V 0 * Cos θ V Y0 = V 0 * Sin θ Step #2: Calculate the maximum height. How far up did it go?

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ESS 303 – Biomechanics

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  1. ESS 303 – Biomechanics Projectiles

  2. Which Will Hit First? Y = 1/2 at2

  3. Put Things Together (4 Steps) • Step #1: Calculate the X and Y components of movement. • VX0 = V0 * Cos θ • VY0 = V0 * Sin θ • Step #2: Calculate the maximum height. How far up did it go? • Yup = (VY2 – VY02)/2a • Ydown: How far down will it fall (think about it)?

  4. Put Things Together (4 Steps) • Step #3: Calculate the hang-time • Y = ½at2 • t = √(2Y)/a • Remember to add time up and time down • Step #4: Calculate the range (the horizontal distance) • X = VX0 * t

  5. A Shortcut? v2Sin θCos θ + vCos θ√(vSin θ)2 + 2gh R = –––––––––––––––––––––––––––––––– g

  6. Problems • You drop a penny from the top of a 2000 meter-high building • How long will it take to hit the ground? • How fast will it be going when it hits?

  7. Problems • A player kicked a football giving it a velocity of 20m/s at an angle of 37°. It was caught by another player at a height of 1.5meters. • What were the X and Y components of velocity? • How high did it go? • How long was it in the air? • How far apart were the players?

  8. Quiz 2 Notes • Next week • Bring a calculator (with trig. functions) • Formula sheet provided (same as one on the web) • Scratch paper is recommended • About 16 total points • About 5 problems ranging in points from 2 to 7 • Show your work and include units

  9. Quiz 2 Sample Problems • A runner completes 17 laps of a quarter-mile track. What was his or her distance and displacement? • Distance = 4.25 Miles • Displacement = 0 Miles • Move on a grid from point (3,6) to point (8,10). What are your horizontal, vertical, and resultant displacements? • Horizontal Displacement = 5 • Vertical Displacement = 4 • Resultant Displacement = 6.40

  10. More Quiz 2 Sample Problems • A ballerina twirls 4½ times. What was her angular distance in degrees and radians? • Angular Distance = 1620 Degrees • Angular Distance = 28.27 Radians • While watching a golf swing, you note that the angular velocity at the .18 second mark was 2.5 radians/second. You also see that the angular velocity at the .41 second mark was 12.02 radians/second. What was the angular acceleration? •  = (/t) •  = (12.02-2.5)/.41-.18) = (9.52/0.23) = 41.39 r/s2

  11. 23º YDown = Yup+1.5m Final Quiz 2 Sample Problem • A pitcher throws a ball 1.5 meters above the ground. The ball is released at a 23 degree angle at a velocity of 37 m/s. How far down-field will the ball go (do all 4 steps and show your work)? 37m/s Yup

  12. 23º YDown = Yup+1.5m Final Quiz 2 Sample Problem • Step 1: Horizontal and Vertical Velocities • VX = (V0 * CosӨ) • VX = 34.06 m/s • VY = (V0 * SinӨ) • VY = 14.46 m/s 37m/s Yup

  13. 23º YDown = Yup+1.5m Final Quiz 2 Sample Problem • Step 2: How high did it go (from point of release)? • Y = (Vy02 – Vy12)/(2*a) • Yup = 10.66 meters • Ydown = 12.16 meters 37m/s Yup

  14. 23º YDown = Yup+1.5m Final Quiz 2 Sample Problem • Step 3: What was the flight time? • t = √((2Y)/a) • tup = 1.47 seconds,tdown = 1.57 Seconds • ttotal = 1.47 + 1.57 =3.04 Seconds 37m/s Yup

  15. 23º YDown = Yup+1.5m Final Quiz 2 Sample Problem • Step 4: How far down-field did the ball go? • X = VX * ttotal • X = (34.06 m/s * 3.04 s) =103.54 meters 37m/s Yup

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