Up and Down Left and Right

 Objects Moving In TWO dimensions  Horizontal and Vertical  Projectiles must have displacement, and velocity and acceleration  Each has horizontal (x) and vertical (y) components

 Projectiles will have constant vertical acceleration –9.81m/s 2 on Earth  Projectiles will have constant horizontal velocity  The horizontal displacement (d x ) is called the “range”

 For projectiles, the equations are used twice…  Horizontal components of motion  vertical components of motion

 Objects “fired” Horizontally Initial horizontal velocity is LOCKED at a single value Initial horizontal velocity is LOCKED at a single value Initial vertical velocity is ZERO Initial vertical velocity is ZERO Horizontal Acceleration is ZERO Horizontal Acceleration is ZERO Vertical Acceleration is g Vertical Acceleration is g Displacements, times, and velocities can be determined using equations for motion Displacements, times, and velocities can be determined using equations for motion

 Horizontal projectiles will accelerate downward at the same rate as something that is dropped from the same height  Therefore they hit the ground at the same time!

 A furry bunny rabbit is dropped out of a plane flying horizontally at an altitude of 490 m with a velocity of 250 m/s. The bunny rabbit falls freely to a concrete patio on the ground.  Calculate the time required for the bunny rabbit to hit the ground.  Calculate the horizontal distance covered by the bunny rabbit from drop point to impact point.

 A Chinchilla is released from a plane from 100 m above the ground. The plane was flying along at 22.5 m/s East. How far from the release point above the ground will the ugly rodent land?

 A squirrel is thrown horizontally at 15m/s from the top of a cliff that is 44 m high.  How long does it take for the squirrel to hit the ground  How far from the base of the cliff does the squirrel hit the ground?  How fast is it falling vertically the instant before it explodes all over the ground?

 A prairie dog is being chased by a deranged physicist. It runs away and jumps over the edge of a canyon because it is unintelligent. The rodent was running with a velocity of 10 m/s and it fell 200m to the valley floor.  How long does it take for the ugly prairie dog to hit the ground  How far from the base of the cliff does the rodent hit the ground?  What was the rodent’s horizontal velocity the instant before it explodes all over the ground?

 Objects “fired” at Angles Initial horizontal velocity is LOCKED at a single value Initial horizontal velocity is LOCKED at a single value v ix and v iy are found with TRIG v ix and v iy are found with TRIG a x = ZERO a y = -9.81m/s 2 a x = ZERO a y = -9.81m/s 2 Vertical Acceleration is g Vertical Acceleration is g Max Height Vertical Velocity = ZERO (also ½ flight time) Max Height Vertical Velocity = ZERO (also ½ flight time)

 Draw diagrams of the situations!  45 degrees gives the HIGHEST RANGE!

 To solve for any variable…  determine if it is horizontal or vertical  Use only the horizontal OR only vertical components in an equation  Objects launched at 45° will have a maximum horizontal distance (range)

 A Vole is launched with a slingshot at an angle of 40 degrees. A radar gun clocks the flying rodent at 50 m/s. What is the rodent’s horizontal velocity? What is the rodent’s horizontal velocity? What is the rodent’s vertical velocity? What is the rodent’s vertical velocity? What is the rodent’s total flight time? What is the rodent’s total flight time?

A guinea pig is strapped to a missile and fired with an initial velocity of 300 m/s at an angle of 30.0° above the ground. After a flight time of 30.6 seconds the guinea pig returns to level ground and explodes.  Calculate the initial horizontal and vertical components of the velocity  Calculate the maximum height of the guinea pig above the ground  Calculate how far from the launch site the guinea pig explodes

A chipmunk was launched from a crossbow with an initial velocity of 44.7 m/s at an angle of 66 degrees above the horizontal… a) What was the maximum height reached by the rodent? b) How long did the chipmunk take to return to the launching height (0m) c) How far from the launch position did the chipmunk land and combust?

 Your teacher kicks a woodchuck from ground level with an initial velocity of 27 m/s at 30 degrees above the horizontal. a) Find the hang time of the rodent… b) Find the range (how far away it landed)… c) What was the maximum height reached by the woodchuck?