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
• vertime. 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.

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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 y0 = 2.4 m, then how accurately must he judge the speed of the ball at launch? Some useful parameters are below. Horizontal distance to center of basket: 22 m Basket height: 3.10 m Basket diameter: 0.46 m Ball diameter: 0.239 m

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Turning Around 1 3

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Recall Instantaneous Velocity 4

A B A B A B A B A B Tangent line Letting Δt→0 time (t) position (x)

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Visualizing Projectile Motion 5

r 

1= xi

 + y j  A x y

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Visualizing Projectile Motion 6

r 

1

A x y

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Visualizing Projectile Motion 7

r 

1

A B r 

2

x y

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Visualizing Projectile Motion 8

r 

1

A B r 

2

x y

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Visualizing Projectile Motion 9

r 

1

A B r 

2

Δ r  x y

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Visualizing Projectile Motion 10

r 

1

A B r 

2

Δ r  = Δxi  + Δy j  Δ r  x y

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Visualizing Projectile Motion 11

A B x y

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Visualizing Projectile Motion 12

B A x y

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Visualizing Projectile Motion 13

B A x y

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Visualizing Projectile Motion 14

A B B A B A B A x y

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Visualizing Projectile Motion 15

B A x y

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Visualizing Projectile Motion 16

A B B A B A B A Δ r  Instantaneous velocity v  tangent at A x y

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Visualizing Projectile Motion 17

v  x y

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Be Aware! 18

We’ll use these plots to visualize and analyze motion, but they represent different quantities.

A B A B A B A B A B Tangent line Letting Δt→0 time (t) position (x) A B B A B A B A Δ r  Instantaneous velocity v  tangent at A x y

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Results from Measurement, Uncertainty, and Variation 19

〈g〉=9.2±3.2 m/s 5 10 15 20 0.0 0.5 1.0 1.5 2.0 2.5 3.0 〈g〉 (m/s) Counts Measurement, Uncertainty, and Variation 2020

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Get out of the way 20

The trebuchet at Warwick Cas- tle in the UK is home to one

• f 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 y0 = 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.

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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 y0 = 2.4 m, then how accurately must he judge the speed of the ball at launch? Some useful parameters are below. Horizontal distance to center of basket: 22 m Basket height: 3.10 m Basket diameter: 0.46 m Ball diameter: 0.239 m

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Measurement and Uncertainty 22

True value

Same number of measurements with different standard deviations Same average

x Number of Measurements Average and Standard Deviation

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Precision versus Accuracy 23

Not precise. Precise, but not accurate. Precise and accurate.

True value x Number of Measurements Average and Standard Deviation True value x Number of Measurements Average and Standard Deviation True value x Number of Measurements Average and Standard Deviation

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Understanding some Statistics 24

x Number of Measurements Average and Standard Deviation

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Understanding some Statistics 25

True value σ σ x Number of Measurements Average and Standard Deviation

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Understanding some Statistics 26

True value σ σ 68% of area x Number of Measurements Average and Standard Deviation

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Lab Results 27

Projectile (2019, m/s2) Projectile (2018, m/s2) 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

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Lab Results 28

Freefall (m/s2) Projectile (m/s2) 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

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