PROJECTILE MOTIONPROJECTILE MOTION

Terms of ReferenceTerms of Reference

Angle of projectionAngle of projection Velocity of projectionVelocity of projection TrajectoryTrajectory Greatest heightGreatest height RangeRange Time of flightTime of flight

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Characteristics & AssumptionsCharacteristics & Assumptions

Planar motionPlanar motion Air resistance: negligibleAir resistance: negligible Gravity: downwardGravity: downward No horizontal accelerationNo horizontal acceleration Constant vertical accelerationConstant vertical acceleration Parabolic trajectoryParabolic trajectory Independent horizontal and vertical motionsIndependent horizontal and vertical motions

Monkey & Hunter ExperimentMonkey & Hunter Experiment

Experimental VerificationExperimental Verification

Computer simulation

Analysis of Projectile MotionAnalysis of Projectile Motion Video 1Video 1

Analysis of Projectile MotionAnalysis of Projectile Motion

Video 2Video 2

Analysis of Projectile MotionAnalysis of Projectile Motion

Motion Horizontal Vertical

InitialVelocity

u cos u sin

Acceleration 0 -g(-ve for

downwards)

Time taken t t

Distancemoved

x = ut cos y = ut sin -gt2/2

FinalVelocity

u cos u sin - gt

Graphs for a Projectile MotionGraphs for a Projectile Motion

Greatest Height Greatest Height hh

g

αuh

2

sin 22

at g

ut

sin

Time of FlightTime of Flight

g

uT

sin2

Range RRange R

g

uR

2sin2

Maximum horizontal range:g

uR

2

max

when 45Simulation

TrajectoryTrajectory

22

2

cos2tan

u

gxxy

Or

xg

uy

222 cos2

Terminal VelocityTerminal Velocity

Sky-diver in free fallSky-diver in free fall

Terminal VelocityTerminal Velocity

AbcAbc

Terminal velocity is reached when f(v) = g

Terminal Velocity: v-t GraphTerminal Velocity: v-t Graph

EXAMPLESEXAMPLES