KIN 3309 1nd Edition Lecture 10 Outline of Last Lecture I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX XX XXI XXII Human Movement Analysis Movements Occur Over Time Important Parameters Velocity v Velocity slope Velocity Estimation Finite Differentiation Instantaneous Velocity Average vs Instantaneous Velocity Graphical Example Constant Velocity Acceleration Instantaneous Acceleration Constant Acceleration Integration Finite Integration Example Riemann Sum Kinematic Analysis Gait Kinematics How to Solve Kinematics Problems Quiz Outline of Current Lecture I II III IV V VI VII What is a Projectile Projectile Motion Factors Influencing Projectiles Factors Affecting Trajectory Dropping Something Equations of Motion Tossing an Object Straight Up These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute VIII IX X XI XII XIII XIV Two Dimensions How Far Will it Go Problem Two Dimensions Initial Angle Problem Range Flat Ground Problem Range Uneven Ground Problem Quiz Current Lecture I What is a Projectile a An object that is only acted on by i Gravity ii Air resistance we will ignore today b We have no control over the object once we lose contact with it c Thrown implements balls discus shot and airborne humans long jump high jump can be projectiles II Projectile Motion a b What do we want to control i How far how long how high c III Factors Influencing Projectiles a Gravity b Air resistance i Air resistance is often negligible ii Air resistance is considered negligible in this section of the text c No other forces can influence the flight trajectory of the projectile IV Factors Affecting Trajectory a V VI Dropping Something a E g a hockey puck onto the ice i What acceleration do we use ii What is the initial velocity iii What is the initial vertical position b The velocity increases as the puck falls c Thus as the puck moves farther from its initial starting position the faster it goes Equations of Motion a b VII Tossing an Object Straight Up a Part one going up b Say vi 2 m s c Lets explore by using i d Note that at some point v 0 i What is that point 1 The peak of the trajectory The highest point of the path ii How high does it go 1 2 10ths of a meter iii How long is it in the air 1 2 10ths of a second e How would we make it go higher VIII Two Dimensions a Usually we don t only care about how high something goes i Even pole vaulters and high jumpers don t go straight up they have to move forward b We usually want something to go a particular distance or as far as possible i A free throw a kick off ii Shot put long jump c Horizontal and vertical components are independent d The parabolic trajectory of projectiles i Vertical velocity is zero at peak height ii Horizontal velocity is unchanged iii Peak height occurs at total horizontal distance and at total time when starting and ending at the same height iv No new equations v Just remember to designate x and y variables 1 Also seen as h and v for horizontal and vertical IX How Far Will it Go Problem a Kick a soccer ball given the initial the following characteristics i 15 m s horizontal velocity 10 m s vertical velocity ii b Break it into up and down parts of the trajectory i Solve for tup using 1 ii Solve for total time peak height occurs at total time so 1 iii Solve for pf using 1 c X Two Dimensions a The parabolic trajectory of projectiles i Vertical velocity is zero at peak height ii Horizontal velocity is unchanged iii Peak height occurs at total horizontal distance and at total time when starting and ending at the same height XI Initial Angle a Often you will be given the initial angle theta and the total velocity vtot i Instead of the initial horizontal and vertical velocities b c d Kick a football at 30 degrees and 30 m s i Calculate ii XII Range Flat Ground Problem a b Kick a soccer ball given the initial the following characteristics i 15 m s horizontal velocity 10 m s vertical velocity 1 XIII ii Range Uneven Ground Problem a This time the same football is kicked from the roof of a garage height 1 76m b c d e XIV Quiz a A valuter is trying to reach a velocity of 7 m s at the end of 14 m runway How quickly must he accelerate i 0 50 m s2 ii 1 75 m s2 iii 2 00 m s2 iv 3 50 m s2 b A child s vertical takeoff velocity when jumping on a trampoline is 5 3 m s Assuming takeoff and landing heights are the same how long is the child airborne i 0 29 s ii 0 54 s iii 1 08 s iv 1 85 s c A shot putter throws the shot with a horizontal velocity of 10 m s and a vertical velocity of 10 m s from a height of 2 0 m Calculate the range of the throw i 22 2