Projectile Motion characteristics and analysis procedures Objectives –Review characteristics of projectile motion (pp ) –Review factors influencing projectile motion –Present and explain calculation methods for analyzing projectile motion Homework – due Monday, Sept 13 –Problems 7,9,10 on page 347

Projectile motion characteristics It is a freely falling body, subject to only two forces – gravity and wind resistance May be dropped, or projected (1) vertically, (2) horizontally, or (3) obliquely Flight pattern is determined by initial velocity –Speed (V 0 ) –Direction (  )

Projectile motion (cont’d)

Projectile motion, cont;d

Projectile motion, cont’d Ignoring air resistance, flight pattern is parabolic

Projectile motion, cont’d Effect of angle of projection on flight pattern

Projectile motion, cont’d If projection angle is constant, range increases directly with magnitude of velocity

Projectile motion, cont’d Projectile height plays a role in optimal projection angle for horizontal distance

Projectile motion, cont’d Resolving projectile motion into vertical and horizontal components – the first step in calculating motion parameters of interest V vert = V sin  V horiz = V cos 

Projectile motion equations –Maximum height when given time of flight (hw prob #7) h = ½ at 2, where t = ½ total flight time –Maximum height when given initial velocity (hw prob #9) –Time of flight when given initial velocity (hw probs # 9, 10) –Range, or horiz dist when given initial Velocity (hw probs 9,10) –If time is calculated first, using above equation (hw probs 9,10) this reduces to: D horiz = V horiz T = V cos  T

Kin 330 Projectile problem : Find maximum height of a projectile when flight time (T) is known. Note that liftoff and landing heights must be the same for this formula to apply. If the total flight time of a ball thrown upward is 3 s, how high does it go above liftoff height?

Kin 330 Projectile problem : Find time of flight, range, and max ht when initial velocity and height above ground are known A softball is released at a velocity of 24 m/s at a height above ground of 2 m at an angle of 40 degrees. Find: a) tme of flight, b) range, and c) maximum height. Solution:

Summary This chapter introduced basic concepts related to kinetics Several types of mechanical loads act on the human body. The distribution of force within a body structure is termed mechanical stress. Vectors quantities have magnitude & direction Vector problems may be solved by a graphic or a trigonometric approach. Kinematic concepts related to projectile motion were introduced Calculation methods for total body COM were presented