Projectile Motion

Combining Motion and Vector concepts2D MotionMoving Motion ForwardVelocity, Displacement and Acceleration are VECTORSVectors have magnitude AND directionSo far, direction has been positive and negativeMotion with VectorsMotion concepts combine with Vector concepts to allow us to represent motion in multiple directions simultaneouslyTwo (2) major concepts will be addressed:1. Moving in two directions at once (e.g. projectiles)2. Moving with respect to (wrt) a non-stationary object (relative motion)How High How Far2nd significant project of semesterLaunch an objectMeasure distance and timeCalculate everything elseTake video or picturesUpload to Gaggle or Edmodo (zdm2ni)Two daily grades (undroppable)Due Tuesday, October 29th What is Projectile Motion?

Projectile MotionTwo-dimensional motion of an objectVerticalHorizontal

ProjectilesAirborne objects that move as a result of their own inertia and gravity.They exhibit two dimensional motion.Horizontal and vertical motionHorizontal and vertical motion are independent of one another.The resultant motion is a combination of horizontal and vertical motion.

Components of Projectile MotionProjectiles have: vertical velocities that increase and decrease because they are influenced by gravitational forces.horizontal velocities remain constant because they are not influenced by gravitational forces.Types of Projectile MotionHorizontalMotion of a ball rolling freely along a level surfaceHorizontal velocity is ALWAYS constantVerticalMotion of a freely falling objectForce due to gravityVertical component of velocity changes with timeParabolicPath traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity

Displacement for Projectiles

Examples of Projectile Motion

Launching a Cannon ballSimulators and examplesMusic analogy

http://www.geogebra.org/en/upload/files/nikenuke/projectile06d.htmlhttp://www.cs.utah.edu/~zachary/isp/applets/Cannon/Cannon.html

Velocity SplitsHave a fixed starting velocitySplits between X and Y initial velocities using Triangle rules

Horizontal (X) motionX-distance is called RangeMoves at constant velocity/speed/ratei.e. ZERO acceleration

VTOTALVXVYVertical (Y) MotionY-direction called HeightY velocity changes (accelerates) because of Gravity (g)= - 9.8 m/s2 -10 m/s2Y velocity (speed) stops (=0) at top of trajectoryReturns to same magnitude but different sign when returns to launch level

VTOTALVXVY

Horizontally Launched ProjectilesRolls off table/cliffThrown/Fired HorizontallyLaunch angle = 0ALL initial velocity is in X direction Vy-initial = 0

Horizontally Launched ProjectilesEquations Simplify

Horizontally Launched ProjectilesSample ProblemA dart gun is fired from a 1.9 meter table and lands 2.8meters from the table. What is the muzzle velocity of the dart gun?How far would the dart travel if fired from 2.3 m?

Horizontally Launched ProjectilesSample ProblemA dart gun is fired from a 1.9 meter table and lands 2.8meters from the table. What is the muzzle velocity of the dart gun?How far would the dart travel if fired from 2.3 m?

Additional official formulasEquations X and Y componentsX- Component

Y- Component

Note: acceleration due to gravity is

Equations Combined (vector)

EquationsX- Component

Y- Component

Vectors

Note: acceleration due to gravity is

Strategies for Applying Kinematic Equations in 2 DimensionsMake a drawing of the situation.Decide which directions to be called positive and negative. Do this for both the x and y directions.Remember that the time variable is the same for both x and y.Make note of all the assumed information.Starts at rest.StopsWhen motion is divided into two segments, remember the final velocity for one segment becomes the initial velocity for the next segment.Keep in mind there might be two possible answers form the same problem. Choose the answer that matches the physical situation at hand.Factors Affecting Projectile MotionWhat two factors would affect projectile motion?AngleInitial velocity

Initial VelocityAngleLaunch AngleLaunch Angle to maximize distance is 45Complementary angles (add up to 90) will launch to the same horizontal distanceClass ExerciseAn object is fired from the ground at 100 meters per second at an angle of 30 degrees with the horizontalCalculate the horizontal and vertical components of the initial velocityAfter 2.0 seconds, how far has the object traveled in the horizontal direction?How high is the object at this point?ApplicationsAny Ideas?SolutionPart a

Part b

Part c

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