PROJECTILE MOTION• What happens when you launch the bird at a large angle with respect to the ground? Why would you want to do this?• What happens when you launch the bird at a smaller angle with respect to the ground? Why would you want to do this?
PROJECTILE MOTION• Definition: Two-dimensional motion of an object • Free-fall with an initial horizontal velocity • Projectile follows a parabolic path• There is both horizontal and vertical motion • Vertical motion is influenced by gravity • Horizontal motion is constant• Examples: golf, soccer, archery, football, etc.
PROJECTILE MOTION• The path (trajectory) of a projectile is a parabola• Projectile: Any object which projected by some means and continues to move due to its own inertia (mass). www.physicsclassroom.com
EXPERIMENTWhat do you think? Which ball will hit the ground first?a) The left ball will hit firstb) The right ball will hit firstc) They will hit the ground at the same time.
PROJECTILE MOTION • Recall that velocity is a vector! • There are two components for the vectors velocity – horizontal (vx) and vertical (vy) • Horizontal and vertical are perpendicular to one another and are independent of each other. Vx is CONSTANTVy is influenced by gravity (Free-fall motion!)
PROJECTILE MOTION• What do you notice here about the displacement of the projectile in the x & y directions? • X: direction: displacement is the SAME every second! • Y: displacement INCREASES every second
PACKAGE DROP • The package follows a parabolic path and remains directly below the plane at all times • The vertical velocity changes (faster, faster) • The horizontal velocity is constant!
HORIZONTALLY LAUNCHED PROJECTILES Projectiles which have NO upward trajectory and NO initial VERTICAL velocity. vox vx constantvoy 0m/ s
HORIZONTALLY LAUNCHED PROJECTILESTo find the horizontal and vertical displacements:• Need two equations: One for the “x” direction and one for the “y” direction.• use our kinematic equations xf = xi + vit + 0.5at2 x X-direction: x =oxtxit vv y-direction: y = 0.5ayt2Remember, the velocity is Remember that since the projectileCONSTANT horizontally, so that is launched horizontally, the INITIALmeans the acceleration is ZERO! VERTICAL VELOCITY is equal to ZERO.
HORIZONTALLY LAUNCHED PROJECTILESTo find the horizontal and vertical velocities:• Need two equations: One for the “x” direction and one for the “y” direction.• use our kinematic equations vf = vi + at X-direction: vxfv= t xi x ox v y-direction: vyf = vyi + ayt OR vyf2 = vyi2 – 2ayΔy
HORIZONTALLY LAUNCHED PROJECTILES Example: A plane traveling with a What do I What I want to horizontal velocity of 100 m/s is know? know? 500 m above the ground. At some point the pilot decides to drop vox=100 m/s t=? some supplies to designated target below. y = 500 m x=? (a) How long are the supplies in the air? voy= 0 m/s (b) How far away from point where it g = -9.8 m/s/s was launched will it land?(a) y = 0.5ayt2 -500 = 0.5(-9.80)t2 t2= 102.04 t = 10.1 seconds (b) x = vxit = (100)(10.1) = 1010 m
PROJECTILES: LET’S REVISIT THIS VIDEO… • Why did they land at the same time?• As soon as both balls are released, they are in “free fall”• Even if a marble is given an initial horizontal velocity, its initial vertical velocity is still zero and only gravity is influencing it in the y-direction…just like it is for a marble in free-fall motion!