2 N I S C I T KINEMA

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2 N I S C I T KINEMA S N O I T C

2 N I S C I T KINEMA S N O I T C E DIR CHAPTER 3

KINEMATICS IN TWO DIMENSIONS

KINEMATICS IN TWO DIMENSIONS

KINEMATIC EQUATIONS AND VARIABLES X component Variable Y component x Displacement y ax Acceleration

KINEMATIC EQUATIONS AND VARIABLES X component Variable Y component x Displacement y ax Acceleration ay vx Velocity final vy Vx 0 Velocity initial vy 0 t time t vx = vx 0 + ax t x = ½ (vx 0 + vx) t vy = vy 0 + ay t y = ½ ( vy 0 + vy) t x = x 0 + vx 0 t + ½ ax t 2 y = y 0 + vy 0 t + ½ ay t 2 vx 2 = vx 02 + 2 ax (x-x 0) vy 2 = vy 02 + 2 ay (y-y 0)

TO REMEMBER: • THE MOTION IN THE X WOULD OCCUR EXACTLY AS IT WOULD

TO REMEMBER: • THE MOTION IN THE X WOULD OCCUR EXACTLY AS IT WOULD IF THE Y PART DID NOT EXIST • THE MOTION IN THE Y WOULD OCCUR EXACTLY AS IT WOULD IF THE X PART DID NOT EXIST • X AND Y MOTION ARE INDEPENDENT OF EACH OTHER

PROJECTILE MOTION: • PROJECTILE : A PROPELLED OBJECT THAT TRAVELS THROUGH THE AIR BUT

PROJECTILE MOTION: • PROJECTILE : A PROPELLED OBJECT THAT TRAVELS THROUGH THE AIR BUT HAS NO CAPACITY TO PROPEL ITSELF. • OBJECTS MOVES IN BOTH X AND Y DIRECTION • PROJECTILE MOTION: THE MOVEMENT OF A PROJECTILE AS IT TRAVELS THROUGH THE AIR, INFLUENCED ONLY BY ITS ORIGINAL VELOCITY AND GRAVITATIONAL ACCELERATION.

HORIZONTAL PROJECTILE MOTION: • A BALL ROLLING ACROSS A TABLE WITH A CONSTANT VELOCITY

HORIZONTAL PROJECTILE MOTION: • A BALL ROLLING ACROSS A TABLE WITH A CONSTANT VELOCITY • AS THE BALL ROLLS OFF THE TABLE IT CONTINUES ITS HORIZONTAL MOTION, YET ALSO ACCELERATES VERTICALLY. RESULT IS A CURVED MOTION • A PACKAGE BEING DROPPED FROM A CRUISING AIRPLANE WOULD BE ANOTHER TYPICAL PROBLEM TYPE

EXAMPLE: •

EXAMPLE: •

SOLUTION: •

SOLUTION: •

NOTES: •

NOTES: •

CONCEPTUALLY: •

CONCEPTUALLY: •

PROJECTILE MOTION AT AN ANGLE: • A BALL IS KICKED IN THE AIR FOR

PROJECTILE MOTION AT AN ANGLE: • A BALL IS KICKED IN THE AIR FOR A FIELD GOAL • THE KICKER GIVES THE BALL AN INITIAL VELOCITY AT AN ANGLE (SO BOTH VERTICAL AND HORIZONTAL) • A CANNON LAUNCHING A CANNONBALL WOULD BE ANOTHER TYPICAL EXAMPLE

EXAMPLE: •

EXAMPLE: •

EXAMPLE: •

EXAMPLE: •

SOLUTION: •

SOLUTION: •

NOTES: • WE FIND THE INITIAL VELOCITIES USING SINE AND COSINE. • TIME IS

NOTES: • WE FIND THE INITIAL VELOCITIES USING SINE AND COSINE. • TIME IS THE “BRIDGE” BETWEEN THE X AND Y DIRECTION • THERE IS SYMMETRY – HALFWAY POINT IS THE HIGHEST POINT. • PROBLEMS COULD ASK YOU TO FIND “HANG TIME”, MAXIMUM HEIGHT, ETC.