2 Objectives and Essential Questions Apply definitions of displacement, velocity, and acceleration as they relate to two dimensionsDemonstrate proficiency in problem solving using kinematic equations as they apply to motion in two dimensionsPredict the horizontal displacement of a projectile launched horizontally (Laboratory)Essential QuestionsHow can we describe motion in two dimensions?How can we predict motion in two dimensions?
3 The DefinitionA projectile is any object that is projected and continues to move dueto its own inertiaGravity is the only item actingon the objectThrown atan angleVerticallydownwardVerticallyupward
4 The Motion of a Projectile - Horizontal In the absence of gravity, a projectile will travel at the same speedand in the same directionGravity is unable to effectthe horizontal motion ofa projectile
5 The Motion of a Projectile - Vertical Gravity only plays a role in the verticaldirection of projectiles – accelerates the objectGravity-freepath
6 Combining the Components Together, these components produce what is called a trajectory or path. This path is parabolic in nature.ComponentMagnitudeDirectionHorizontalConstantVerticalChanges
7 Horizontally Launched Projectiles Projectiles which have NO upward trajectory and NO initial VERTICAL velocity.
8 Horizontally Launched Projectiles To analyze a projectile in 2 dimensions we need 2 equations. One for the “x” direction and one for the “y” direction.Remember, the velocity is CONSTANT horizontally, so that means the acceleration is ZERO!Remember that since the projectile is launched horizontally, the INITIAL VERTICAL VELOCITY is equal to ZERO.
9 Horizontally Launched Projectiles Example: A plane traveling with a horizontal velocity of 100 m/s is 500 m above the ground. At some point the pilot decides to drop some supplies to designated target below. (a) How long is the drop in the air? (b) How far away from point where it was launched will it land?What do I know?What I want to know?vox=100 m/st = ?y = 500 mx = ?voy= 0 m/sg = -9.8 m/s/s1010 m10.1 seconds
10 Vertically Launched Projectiles NO Vertical Velocity at the top of the trajectory.Vertical Velocity decreases on the way upwardVertical Velocity increases on the way down,Horizontal Velocity is constantComponentMagnitudeDirectionHorizontalConstantVerticalDecreases up, top, Increases downChanges
11 Vertically Launched Projectiles Since the projectile was launched at a angle, the velocity MUST be broken into components!!!vovoyqvox
12 Vertically Launched Projectiles There are several things you must consider when doing these types of projectiles besides using components. If it begins and ends at ground level, the “y” displacement is ZERO: y = 0
13 Vertically Launched Projectiles You will still use kinematic equations, but YOU MUST use COMPONENTS in the equation.vovoyqvox
14 ExampleA place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.(a) How long is the ball in the air?(b) How far away does it land?(c) How high does it travel?vo=20.0 m/sq = 53
15 ExampleWhat I knowWhat I want to knowvox=12.04 m/st = ?voy=15.97 m/sx = ?yo = 0ymax=?g = m/s/sA place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.(a) How long is the ball in the air?3.26 s
16 ExampleA place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.(b) How far away does it land?What I knowWhat I want to knowvox=12.04 m/st = 3.26 svoy=15.97 m/sx = ?y = 0ymax=?g = m/s/s39.25 m
17 Example What I know What I want to know t = 3.26 s x = 39.25 m y = 0 vox=12.04 m/st = 3.26 svoy=15.97 m/sx = my = 0ymax=?g = m/s/sA place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.(c) How high does it travel?CUT YOUR TIME IN HALF!13.01 m