Projectile Motion Projectile object that is launched thrown

Projectile Motion Projectile- object that is launched, thrown, or fired in the air that is in a state of free fall Trajectory- the path the projectile follows. - projectile motion is described in terms of position, velocity, and accelertation. - The horizontal and vertical components of velocities are independent of each other. • Parabolic – Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity Range – the horizontal distance from the point of release. R = range

Examples of projectiles

Projectile Motion • Two-dimensional motion of an object – Vertical – Horizontal We use a t-chart to represent the two motions: X (horizontal) Y (vertical)

Types of Projectile Motion • Horizontal – Motion of a ball rolling freely along a level surface – Horizontal velocity is ALWAYS constant • Vertical – Motion of a freely falling object – Force due to gravity – Vertical component of velocity changes with time

Examples of Projectile Motion • Launching a Cannon ball

Projectile motion • What velocity will horizontal projectiles have? • What acceleration will projectiles have vertically? What will the velocity look like?

Horizontal Components dx = horizontal displacement vx = horizontal velocity t = time dx =vxt notice that there is no acceleration. Why?

Vertical Components g = gravity dy = vertical displacement viy = initial vertical velocity vfy = final vertical velocity t = time

What is the common variable in the horizontal and vertical components?

Example A stone is thrown horizontally at a speed of 5. 0 m/s from the top of a cliff 78. 4 m high. How long does it take the stone to reach the bottom of the cliff? T= ?

Example A steel ball rolls with a constant velocity across a tabletop 0. 950 m high. It rolls off the table and hits the ground 0. 352 m from the edge of the table. How fast was the ball rolling just as it left the table?

Example Divers at Acapulco dive horizontally from a cliff that is 65 meters high. If the rocks below the cliff protrude 27 meters beyond the edge of the cliff, what is the minimum horizontal velocity needed to safely clear the rocks below?

Example of a horizontally launched projectile • A cannon is fired horizontally at 20 m/s on a 10 m tall cliff. How long will the cannon ball be in the air? How far from the base of the cliff will the cannon ball fall?

Example problem • An airplane is flying horizontally with a velocity of 250 m/s. • If the pilot drops a water balloon out of the window and it lands a horizontal distance of 500 m from the launch point. • From what height was it dropped?