1. Projectile Motion The motion of a falling object with air resistance and gravity acting on it

2. Projectiles A projectile is any object upon which the only force is gravity Projectiles travel with a parabolic trajectory due to gravity There are no horizontal forces and no horizontal acceleration on projectiles

3. Projectiles The horizontal velocity of a projectile is constant The vertical acceleration of a projectile is caused by gravity and is 9.8m/s/s down The horizontal and vertical motion of a projectile are independent of each other

4. Projectile Motion A force is not required to keep an object in motion A force is required to maintain acceleration If a projectile is moving upward there is a downward force and downward acceleration The object is moving upward and slowing down

5. Gravity and vertical acceleration Gravity only causes a vertical acceleration Gravity does not affect the horizontal distance or motion an object travels Gravity will affect the vertical distance and motion of an object only

6. Horizontally launched projectiles There has to be a horizontal force to cause a horizontal acceleration A projectile has a constant horizontal velocity and a downward vertical acceleration (deceleration)

7. Horizontal Projectiles Horizontal MotionVertical Motion ForcesNoYes, gravity AccelerationNoYes, gravity at 9.8m/s/s VelocityConstantChanging by 9.8m/s each second

8. Non-Horizontally Launched Projectiles When the projectile is launched at an angle the path is a parabola If there was no gravity the projectile would continue upward no gravity gravity

9. Vertical Displacement The vertical displacement of an object can be calculated using: y =.5 * g * t 2 (* = multiplied by) y = vertical displacement g = gravity at -9.8m/s/s t = time in seconds Use this equation when an object is dropped from rest – it has no initial vertical velocity

10. Horizontal Displacement The horizontal displacement of a projectile can be calculated using the following: x = v ix * t where x = horizontal displacement in m v ix = initial horizontal velocity in m/s t = time in s In this case there is no initial vertical velocity, since the projectile is launched horizontally

11. Vertical Displacement of an Angled- Launched Projectile To calculate the vertical displacement of a projectile launched at an angle y = v iy * t + 0.5 * g * t 2 y= vertical displacement in m v iy = initial velocity in m/s t = time in s g = gravity, -9.8 m/s/s t = time in s

12. Sample Problem A projectile has an initial velocity v iy of 19.6m/s and a horizontal velocity of 33.9m/s, what is the vertical and horizontal displacement after 1 s? y = v iy * t + 0.5 * g * t 2 y = (19.6m/s) x (1s) + 0.5 x (-9.8m/s/s) x (1s) 2 y = 19.6m/s + (-4.9m) y = 14.7m (vertical displacement) x = v ix * t x = (33.9m/s) x (1s) x = 33.9m (horizontal displacement)