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Unit 4 Review. Kinematics. Kinematics. When air resistance is not taken into consideration, released objects will experience acceleration due to gravity, also known as freefall. Projectile motion can be predicted and controlled using kinematics. Human Cannonball Training.

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kinematics1
Kinematics
  • When air resistance is not taken into consideration, released objects will experience acceleration due to gravity, also known as freefall.
  • Projectile motion can be predicted and controlled using kinematics
slide4

Human Cannonball Training

Speaking the Lingo

Firing Angle (θ) is measured in degrees. It is the angle at which the projectile left the cannon.

Initial Velocity (Vi) is the angular speed of a projectile at the start of its flight.

slide5

Human Cannonball Training

Calculating Initial Velocity

slide6

Human Cannonball Training

Calculating Horizontal Distance

slide7

Human Cannonball Training

Calculating Firing Angle

Not on formula sheet

slide8

Kinematics important info

  • Horizontal Motion:
    • Velocity is constant in X direction!!!

Vix =

slide9

Kinematics important info

  • Vertical Motion:
  • Velocity changes with time due to gravity
  • Viy = Vi sin theta
  • Velocity is zero in the y direction at peak
slide10

Projectile Motion Problem

  • A ball is fired from a device, at a rate of 160 ft/sec, with an angle of 53 degrees to the ground.
slide11

Projectile Motion Problem

  • Find the x and y components of Vi.
  • What is the initial vertical velocity?
  • What is the ball’s range (the distance traveled horizontally)?
slide12

Projectile Motion Problem

Find the x and y components of Vi.

slide13

Projectile Motion Problem

Find the initial vertical velocity.

slide14

Projectile Motion Problem

What is the ball’s range (the distance traveled horizontally)?

Vi = 160 ft/sec

Theta = 53 degrees

G = -32 ft/sec/sec

statistics1
Statistics

The collection, evaluation, and interpretation of data

Engineers use statistics to make informed decisions based

on established principles.

statistics2
Statistics

Statistics

Inferential Statistics

Generalize and evaluate a population based on sample data

Descriptive Statistics

Describe collected data

Statistics is based on both theoretical and experimental data analysis

methods of determining probability
Methods of Determining Probability
  • Empirical
  • Experimental observation Example – Process control
  • TheoreticalUses known elements
  • Example – Coin toss, die rolling
  • SubjectiveAssumptions Example – I think that . . .
probability
Probability

The number of times an event will occur divided by the number of opportunities

Px = Probability of outcome x

Fx = Frequency of outcome x

Fa = Absolute frequency of all events

Expressed as a number between 0 and 1fraction, percent, decimal, odds

Total probability of all possible events totals 1

probability1
Probability

What is the probability of tossing a coin twice and it landing heads up both times?

HH

How many desirable outcomes?

1

HT

How many possible outcomes?

4

TH

TT

law of large numbers
Law of Large Numbers

The more trials that are conducted, the closer the results become to the theoretical probability

Trial 1: Toss a single coin 5 times H,T,H,H,TP = .600 = 60%

Trial 2: Toss a single coin 500 times H,H,H,T,T,H,T,T,……TP = .502 = 50.2%

Theoretical Probability = .5 = 50%