1. AIM: How can we describe the path of an object fired horizontally from a height above the ground? DO NOW: A ball rolls off a table top with an initial horizontal velocity. –Predict and draw the path that the ball will follow. PHYSICSMR. BALDWIN Projectile MotionOctober 24, 2013

2. PROJECTILE MOTION HOW WOULD YOU DESCRIBE A PROJECTILE? A projectile is an object fired either above the ground horizontally or at an angle with respect to the horizontal OR from the ground at an angle with respect to the horizontal. HOW WOULD YOU DESCRIBE THE PATH OF A PROJECTILE? The path of a projectile is always a PARABOLA. WHAT FORCE(S) IS/ARE ACTING ON THE PROJECTILE? The only force (influence) acting on a projectile is GRAVITY. THEREFORE, WHAT DO YOU THINK IS THE ACCELERATION OF THE PROJECTILE? Its only acceleration is the ACCELERATION DUE TO GRAVITY, g (9.80m/s 2 ) always acting downwards.

3. CAN YOU NOW DEFINE A PROJECTILE IN ONE CONCISE SENTENCE? A projectile is an object moving in two dimensions under the influence of the Earth's gravity alone and following a parabolic path.

4. It can be understood by analyzing the horizontal and vertical motions separately. CHECK Looking at the diagram, analyze the horizontal and vertical velocities of the projectile separately.

5. What did you observe? About the velocity in the x-direction? The velocity in the x-direction is constant (never changes). What does that imply? The horizontal motion is uniform/constant. About the velocity in the y-direction? The velocity in the y-direction is increasing. What does that imply? The object is being accelerated downwards. The object is falling with a constant acceleration g.

6. AIM: How can we describe the path of an object fired at an angle w.r.t. the horizontal? DO NOW: A ball is projected up at an angle with respect to the horizontal with an initial velocity. –Predict and draw the path that the ball will follow. PHYSICSMR BALDWIN Projectiles25-Oct-13 θ v

7. Projectile Motion: A different view Two balls start to fall at the same time. The yellow ball has an initial speed in the x-direction. The red ball is just released (dropped). What do you observe as the balls fall? It can be seen that vertical positions of the two balls are identical at identical times, while the horizontal position of the yellow ball increases linearly.

8. Projectile Motion  In projectile motion, the horizontal motion and the vertical motion are independent of each other, neither motion affects the other.  What is the acceleration of the horizontal motion  zero acceleration  What is the acceleration of the vertical motion  constant downward acceleration of g The initial velocities are

9. RECALL FREEFALL MOTION

10. AIM: How can we solve problems involving projectiles? DO NOW: A cannonball is shot out of a cannon at a speed of 20 m/s at an angle of 30 0 to the horizontal. Calculate the horizontal and vertical components of its velocity? Homework: Your homework sheet will be uploaded onto my webpage. Get it from there. Due FRIDAY. PHYSICS MR. BALDWIN Projectile Motion30-Oct-13 30 0 20 m/s

11. CHECK

12. Write out your equations of motion for constant and accelerated motion if you do not have your index card handy.

13. The vertical motion is accelerated motion.  There is a constant downward acceleration g in the vertical direction. The vertical displacement: The velocity: How would you describe the vertical motion of a projectile?

14. Projectile Motion Analyzed  There is NO horizontal acceleration. Therefore, the motion is uniform or constant. Horizontal velocity never changes How would you describe the horizontal motion of a projectile?  The horizontal distance of a projectile is called the RANGE

15. CHECK What is the acceleration of a projectile? –Always constant g &acting downwards What is meant by the range of a projectile? –Maximum horizontal distance What is meant by the maximum height of a projectile? –Height at which the object stops rising What happens at the maximum height of a projectile? Is the object still moving? –Yes. Horizontally. What is meant by the time of flight of a projectile? –The length of time the object is in the air

16. A cannonball is shot out of a cannon at a speed of 20 m/s at an angle of 30 0. What are the horizontal and vertical components of its velocity? What maximum height did it reach? How long was it in the air? How far did it travel? LET’S ANALYZE THE DO NOW 30 0 20 m/s

17. Vertically, what do we know?

18. Horizontally, what do we know? CHECK. Why do you think that is so?

19. LET’S PLAY HIT THE TARGET. 19 http://phet.colorado.edu/sims/projectile- motion/projectile-motion_en.html http://jersey.uoregon.edu/vl ab/block/Block.html

20. 3-6 Solving Problems Involving Projectile Motion 1. Read the problem carefully, and choose the object(s) you are going to analyze. 2. Draw a diagram. 3. Choose an origin and a coordinate system. 4. Decide on the time interval; this is the same in both directions, and includes only the time the object is moving with constant acceleration g. 5. Examine the x and y motions separately.

21. Solving Problems Involving Projectile Motion 6. List known and unknown quantities. Remember that v x never changes, and that v y = 0 at the highest point. 7. Plan how you will proceed. Use the appropriate equations; you may have to combine some of them.

22. Projectile Motion Is Parabolic In order to demonstrate that projectile motion is parabolic, we need to write y as a function of x. When we do, we find that it has the form: This is indeed the quadratic equation for a parabola.