Its Aint Over Till Its Over! 1 On January 31, 2005 Randolph-Macon - PowerPoint PPT Presentation

It’s Ain’t Over Till It’s Over! 1 On January 31, 2005 Randolph-Macon College (RMC) was playing Guilford College in basketball at Randolph-Macon in Ashland, Virginia. The teams are tied 88-88 with just a fraction of a second in overtime. RMC in yellow sinks a free throw to win the game (at least they thought they won). The second free throw is missed. Jordan Snipes from Guilford (in purple) rebounds the ball and gets a shot off just milliseconds before the buzzer. The rest is history. Jerry Gilfoyle It Ain’t Over Till It’s Over 1 / 28

How hard is this? 2 Consider the accuracy of the shot by Snipes. If he released the ball at an angle θ = 35 ◦ to the horizontal and from an initial height above the floor y 0 = 2 . 4 m , then how accurately must he judge the speed of the ball at launch? Some useful parameters are below. Horizontal distance 22 m to center of basket: Basket height: 3 . 10 m Basket diameter: 0 . 46 m Ball diameter: 0 . 239 m Jerry Gilfoyle It Ain’t Over Till It’s Over 2 / 28

Turning Around 1 3 Jerry Gilfoyle It Ain’t Over Till It’s Over 3 / 28

Recall Instantaneous Velocity 4 Tangent line B B B A A A A A B position ( x ) B Letting Δ t → 0 time ( t ) Jerry Gilfoyle It Ain’t Over Till It’s Over 4 / 28

  Visualizing Projectile Motion 5 A y  + y j 1 = x i r x Jerry Gilfoyle It Ain’t Over Till It’s Over 5 / 28

 Visualizing Projectile Motion 6 A y r 1 x Jerry Gilfoyle It Ain’t Over Till It’s Over 6 / 28

  Visualizing Projectile Motion 7 A B y r 1 r 2 x Jerry Gilfoyle It Ain’t Over Till It’s Over 7 / 28

  Visualizing Projectile Motion 8 A B y r 1 r 2 x Jerry Gilfoyle It Ain’t Over Till It’s Over 8 / 28

   Visualizing Projectile Motion 9 A Δ r B y r 1 r 2 x Jerry Gilfoyle It Ain’t Over Till It’s Over 9 / 28

    Visualizing Projectile Motion 10  = Δ x i  + Δ y j Δ r A Δ r B y r 1 r 2 x Jerry Gilfoyle It Ain’t Over Till It’s Over 10 / 28

Visualizing Projectile Motion 11 A B y x Jerry Gilfoyle It Ain’t Over Till It’s Over 11 / 28

Visualizing Projectile Motion 12 A B y x Jerry Gilfoyle It Ain’t Over Till It’s Over 12 / 28

Visualizing Projectile Motion 13 A B y x Jerry Gilfoyle It Ain’t Over Till It’s Over 13 / 28

Visualizing Projectile Motion 14 B A A A A B B B y x Jerry Gilfoyle It Ain’t Over Till It’s Over 14 / 28

Visualizing Projectile Motion 15 B A y x Jerry Gilfoyle It Ain’t Over Till It’s Over 15 / 28

 Visualizing Projectile Motion 16 Instantaneous velocity  tangent at A B v A A A A B B Δ r B y x Jerry Gilfoyle It Ain’t Over Till It’s Over 16 / 28

 Visualizing Projectile Motion 17 v y x Jerry Gilfoyle It Ain’t Over Till It’s Over 17 / 28

 Be Aware! 18 We’ll use these plots to visualize and analyze motion, but they represent different quantities. Instantaneous velocity Tangent line  tangent at A B A A A A B v B B B B A A A A A B position ( x ) Δ r B B y Letting Δ t → 0 time ( t ) x Jerry Gilfoyle It Ain’t Over Till It’s Over 18 / 28

Results from Measurement, Uncertainty, and Variation 19 Measurement, Uncertainty, and Variation 2020 3.0 2.5 〈 g 〉 = 9.2 ± 3.2 m / s 2.0 Counts 1.5 1.0 0.5 0.0 0 5 10 15 20 〈 g 〉 ( m / s ) Jerry Gilfoyle It Ain’t Over Till It’s Over 19 / 28

Get out of the way 20 The trebuchet at Warwick Cas- tle in the UK is home to one of the world’s largest working siege engines. It takes eight men half an hour to load and re- lease. On 21 August 2006, the trebuchet launched a projectile weighing 13 kilograms (29 lb) at a record speed of 54 m / s (121 mph). If the height of the pro- jectile at launch is y 0 = 20 m and the launch angle is θ = 30 ◦ , then how far does it go before it lands? Assume there is no air friction and the ground is flat. Jerry Gilfoyle It Ain’t Over Till It’s Over 20 / 28

How hard is this? 21 Consider the accuracy of the shot by Snipes. If he released the ball at an angle θ = 35 ◦ to the horizontal and from an initial height above the floor y 0 = 2 . 4 m , then how accurately must he judge the speed of the ball at launch? Some useful parameters are below. Horizontal distance 22 m to center of basket: Basket height: 3 . 10 m Basket diameter: 0 . 46 m Ball diameter: 0 . 239 m Jerry Gilfoyle It Ain’t Over Till It’s Over 21 / 28

Measurement and Uncertainty 22 Average and Standard Deviation True value Number of Measurements Same number of measurements with different standard deviations Same average x Jerry Gilfoyle It Ain’t Over Till It’s Over 22 / 28

Precision versus Accuracy 23 Not precise. Precise, but not accurate. Precise and accurate. Average and Standard Deviation Average and Standard Deviation Average and Standard Deviation True value True value True value Number of Measurements Number of Measurements Number of Measurements x x x Jerry Gilfoyle It Ain’t Over Till It’s Over 23 / 28

Understanding some Statistics 24 Average and Standard Deviation Number of Measurements x Jerry Gilfoyle It Ain’t Over Till It’s Over 24 / 28

σ σ Understanding some Statistics 25 Average and Standard Deviation True value Number of Measurements x Jerry Gilfoyle It Ain’t Over Till It’s Over 25 / 28

σ σ Understanding some Statistics 26 Average and Standard Deviation True value Number of Measurements 68 % of area x Jerry Gilfoyle It Ain’t Over Till It’s Over 26 / 28

Lab Results 27 Projectile (2019, m / s 2 ) Projectile (2018, m / s 2 ) 11.92 12.19 11.078 9.89 11.4 12.06 9.82 14.13 12.55 11.90 11.68 9.79 10.43 10.62 13.29 11 . 2 ± 0 . 9 11 . 7 ± 1 . 5 Jerry Gilfoyle It Ain’t Over Till It’s Over 27 / 28

Lab Results 28 Freefall ( m / s 2 ) Projectile ( m / s 2 ) 10.34 12.19 11.04 9.89 13.11 12.06 11.90 14.13 11.6 11.90 9.84 9.79 9.94 10.62 13.72 13.29 11 . 4 ± 1 . 4 11 . 7 ± 1 . 5 Jerry Gilfoyle It Ain’t Over Till It’s Over 28 / 28