Agenda 1) Warm-Up 5 min 2) Vocab. Words 10 min 3) Projectile Motion fill-in- blank Notes. 15 min 4) New Formulas 5 min 5) Example Problems 15 min 6) Blue “Vector Folder” 10 min 7) Projectile WS 30 min Projectile

Vocab. 1.Maximum height: height of the projectile when the vertical velocity is zero and the projectile has only the horizontal component. 2.Flight time: the time the projectile is in the air; total time spent in the air; “hang” time. 3.Resultant of a projectile: vector which represents the weight or amount of gravity acting on a projectile. 4.Satellite: an object that follows an orbital path around an object and is kept there by only the mutual pull of gravity.

Figure 6-15(Hewitt book) If a projectile had no gravity, it would move with this path:

Gravity pulls the projectile towards the Earth.

Continued: Paths of several projectiles having the same initial speed but different projection angles– all reach different altitudes and have different horizontal ranges or distances traveled horizontally. But, note that the same range is obtained by 2 different projection angles if their angle adds up to 90 degrees.

To find the horizontal distance (d H ) a projectile moves while it is falling, you must know both the horizontal velocity (V H ) and the time the body was in the air (also called total time).

Air resistance is another force that acts on projectiles. It changes the path of a projectile like this:

IDEAL PATH ACTUAL PATH

***If air resistance is small enough to be negligible, a projectile will rise to its maximum height in the same time it takes to fall from that height to the ground (as in free-fall). [Deceleration and acceleration by gravity is equal] **D H = V H (t) Do example problems—see attached

Projectile fired at an Angle: When a projectile is fired at an angle with the horizontal, the principle of independent velocities still holds. The initial velocity of the projectiles can be “resolved” into 2 components. One component is directed vertically and the second is directed horizontally. These components are treated separately when solving problems.

DUE TODAY: Projectile fill-in-blanks (KEEP) Blue “Vector” Unit Folder (11/14/11) DUE NEXT CLASS: Projectile Motion WS (finding horizontal distance) Blue “Vector” Unit Folder (11/14/11) Bring Calculator & Protractor! “There is no better high than discovery.” E. O. Wilson

Projectile fired at an Angle: [red book pg. 158] When a projectile is fired at an angle with the horizontal, the principles of independent velocities still holds. The initial velocity of the projectile can be “resolved” into 2 components. One component is directed horizontally and the second is directed vertically. These are still treated separately. Look at all the vectors on the picture below. There are horizontal vectors, vertical vectors, and diagonal vectors. They are all components of the cannonball’s velocity.

Horizontally: Look at all the horizontal vectors---They are all equally spaced apart. There is still no acceleration in the horizontal direction so the cannonball moves equal horizontal distances in equal time intervals---constant velocity.

Vertically: Look at all the vertical vectors---They get shorter and shorten then disappear at the top of the path, then get longer and longer. This is because there is acceleration vertically (in the direction of the earth’s gravity). The vertical velocity and therefore distance gets bigger and bigger each second the object is still moving. Notice that the horizontal component vector is the same length at any point along the cannonball’s path. The vertical component gets smaller then, disappears then, gets bigger.

These vectors represent the horizontal and vertical component of velocity. The ACTUAL velocity of the object is represented by the diagonal of the parallelogram formed by the components. At the top of the path, the vertical component vanishes, or becomes zero, so the ACTUAL velocity of the cannonball at the top of the path is the exact same as the horizontal velocity at all other points (instead of a combination of the horizontal and vertical).

Gravity acts DOWNWARD So, a ball moving horizontally has NO GRAVITY affecting its velocity.

 The horizontal direction is the x axis. Ignoring drag, there is no force acting on the projectile horizontally.  What keeps the object in MOTION is: Inertia which is present-1 st Law of Newton is being followed.  If the object slows down or stops—it is due to FRICTION.

If that ball is dropped, suddenly gravity acts on it to pull it down. Now it has a vertical component.

 g is constant in magnitude, always in the straight down direction, and always along the y axis; if air resistance is neglected; then, the motion of the center of mass is only due to the force of gravity accelerating or decelerating the mass.

 Projectile motion under the influence of near-Earth--- gravity will produce a curved path.  The vertical direction is on the “y “axis. The only force acting on any projectile vertically will be gravity. The acceleration will be the constant g = m/s 2.

 KEY: What happens to a particle vertically does not affect its horizontal motion. The opposite is also true. The axes are independent.  NOTE what axis is CHANGING!!

Those projectiles that accelerate only in a vertical direction while moving at a constant horizontal velocity have a path that forms a PARABOLA.

 The range is the horizontal distance.  Solve for the time needed for the projectile to reach its maximum height (remember that gravity is acting) by using the “vertical” distance.  Once you know the time of flight, solve for the range by using: D H = Horizontal velocity X Time

 Satellite – an object that falls around Earth or some other body rather than falling into it because of its tremendous speed. ◦ Page 127 (Hewitt book)

TWO DIMENSIONAL MOTION  If no force acts horizontally, the motion found is at constant velocity- due to inertia.  The equation of motion is then D H = V H t.  BUT, to find V H when you have 2- dimensional motion, resolve the initial velocity into its horizontal component by using the formula : V H = V i cos 

 To find V v, resolve the initial velocity into its vertical component.  The formula to do this is: V v = V i sin Ø

 The time an object moves horizontally is the same as the time the object moves vertically.  So, Total time is the “time in the air” for a projectile at-an-angle.

 To find time: Remember that gravity is affecting the motion and therefore, the amount of time the projectile is in the air for “at an angle” will be TOTAL time.  So, t total = V v / g so D H = V H ( t t )

A vertical and a horizontal component. With the trajectory being the initial velocity*

 Acceleration is constant for a projectile.  Speed and velocity change at each point along the parabolic pathway.  What is the speed of the projectile at the very top of its pathway?  What is the acceleration of the projectile at the very top of its pathway?