Projectile Motion

Let’s Review A projectile is an object upon which only force acting is GRAVITY. Remember that the direction of gravity is always DOWNWARD. Types of projectiles: Objects that are dropped Objects that are launched horizontally Objects that are launched upward at an angle

Characteristics The path of a projectile is called a trajectory and is shaped like a parabola. There are two components of motion, horizontal and vertical. These components are independent of one another.

Horizontal Projectiles http://www.physicsclassroom.com/shwave/projectile.cfm A horizontal projectile is launched with an angle of 0o to the horizontal. What have we learned so far? The horizontal velocity is constant. The vertical velocity is changing.

Sum It Up None Gravity, 9.8 m/s2,down Constant Changing   Horizontal Motion Vertical Motion Acceleration Velocity None Gravity, 9.8 m/s2,down Constant Changing

Projectiles Launched at an Angle http://www.nsf.gov/news/special_reports/football/projectile.jsp Once the projectile is launched, the only force acting is Gravity. As with horizontally launched projectiles, the horizontal velocity is constant. The vertical velocity is changing. As the projectile travels upward, the vertical velocity decreases. It reaches 0 m/s at the top of its flight. The vertical velocity increases as the object travels downward. These velocity components can be represented with vectors.

Factors Affecting Projectile Motion How does the initial velocity affect the flight of a projectile? http://www.physicsclassroom.com/shwave/projectile.cfm Initial Velocity Time Distance traveled  20    30  40  50

The greater the initial velocity, the greater the hang time, the longer the horizontal distance

How does the initial velocity effect the flight of a projectile? http://www.physicsclassroom.com/shwave/projectile.cfm Angle Time of flight Horizontal Distance Vertical Distance 20   30 45 60 70 90

Initial Velocity Observations What do you notice about the complimentary angles? They have the same horizontal distance. Which angle produces the maximum range (horizontal distance)? 45 degrees From your observations, which angle produces the maximum height? 70 degrees

Describing Motion with Numbers

Describing Motion with Numbers What was the initial velocity in the upward direction? Let’s determine this velocity using vectors. To do this: Add the vectors graphically. Label all information. Draw the resultant. Use the Pythagorean Theorem to determine the resultant. This is the INITIAL VELOCITY.   To determine the angle, use TRIG functions 22.9 m/s 19.6 m/s 59° 12 m/s

Example 1 cos 60 = vx/40 Vx = 20 m/s Sin 60 = vy/40 Vy = 34.6 m/s A water balloon is launched with a velocity of 40 m/s at an angle of 60 degrees to the horizontal. Draw a picture of the object. Create a right triangle to the horizontal. Label all known information. Solve for the x component. cos ɵ = vx/vi Solve for the y component. sin ɵ = vy/vi 40 m/s 60° cos 60 = vx/40 Vx = 20 m/s Sin 60 = vy/40 Vy = 34.6 m/s