1. Projectile Motion October 2015

2. Free Falling!  So far, we have discussed objects moving along the ground. (walking, driving, etc.)  But we can also discuss the motion of objects flying through the air.  This study is called “Projectile Motion”  Projectile – an object in flight.

3. Free Falling  Objects in flight:  Bullets and arrows  Footballs, baseballs and soccer balls  Raindrops  Gymnasts on trampolines  All of these objects have one major thing in common:  GRAVITY!

4. Free Falling  But is gravity the same for every object?  Is gravity pulling on a baseball the same as a soccer ball?  …a raindrop the same as a gymnast?

5. Free Falling  For a long time, people believed that no, gravity did not treat all objects the same.  They believed the pull of gravity was related to the mass of the object. Large objects tend to “strive harder.”  Remember: Mass = amount of “stuff” in an object.

6. Free Falling  But Galileo Galilei challenged that idea.

7. Free Falling  Galileo (1600s) Dropped objects from the Leaning Tower of Pisa to test his theory.  Theory: All objects fall at the same rate if you account for air resistance.  http://www.youtube.com/watch?v=_Kv-U5tjNCY Pisa http://www.youtube.com/watch?v=_Kv-U5tjNCY  “Proven” on the moon in the late 1960s.  http://www.youtube.com/watch?v=WOvwwO-l4ps Moon http://www.youtube.com/watch?v=WOvwwO-l4ps

8. Free Falling  Using calculations, scientists found that all objects accelerate as they fall at the same rate: 9.8m/s 2

9. Free Falling  The pull of gravity on Mondays, however, is another thing…

10. Free Falling  If Galileo dropped a basketball from the Leaning Tower of Pisa (height = 56 m), how fast was it going when it hit the ground?

11. Free Falling  In the previous problem and equation, did we use mass anywhere? Why or why not?

12. Starter 10/15/13 1. If you ignore air resistance, all falling objects accelerate at a rate of _______. 2. A brick is dropped from a high scaffold.  What is its velocity after 4.0 seconds?  How far does the brick fall during this time?

13. Projectile Motion Day 2 Let’s Review!  What is a “projectile?”  What is the rate of acceleration of an object that is falling?  Does the mass affect the acceleration of an object (ignore air resistance for now.)? Why or why not?  Who discovered this concept and how did he supposedly prove it?  ***If you never made a “formula finder,” or you have already lost yours, MAKE ONE ASAP. You will be using it a LOT!

14. What Goes Up Must Come Down!  Gravity doesn’t just speed up objects that are falling.  If objects are sent upwards, it slows them down at the same rate: 9.8m/s 2

15. Try This!  A tennis ball is thrown straight up with an initial speed of 22.5m/s. It is caught at the same height from which it was thrown.  How high does the ball rise above the height it was released?  How long does the ball remain in the air?

16. Horizontal Projections  Let’s look at objects that are moving both side to side and up and down at the same time. We will start horizontally.

17. Horizontal Projections  Consider the horizontal motion and the vertical motion of the object to be separate.

18. Horizontal Projections  Because the projectile starts with no velocity in the vertical direction, treat it like an object in freefall.

19. Horizontal Projections  The horizontal velocity will affect how far the object travels, horizontally, in the given amount of time.

20. Try This!  A stone is thrown horizontally at a speed of 5.0m/s from the top of a cliff 78.4m high.  How long does it take the stone to reach the bottom of the cliff?  How far from the base of the cliff does the stone hit the ground?  What are the horizontal and vertical components of the stone’s velocity just before it hits the ground?

21. Starter 10/21/13 1.If gravity didn’t exist, what would the path of a projectile look like? 2.A plane flying at 100km/hr accidentally drops a crate of supplies. Where will the crate be, relative to the airplane, when it hits the ground? 3.A batter hits a baseball 60km/hr at a 40 degree angle. If the outfielder catches the ball at the same height it was hit at, how fast is the ball going when it enters the glove?

22. Projectiles at an Angle  So far we have covered:  Horizontal motion  Vertical Motion  Projectiles launched horizontally  Now our final piece:  Projectiles launched at an angle!

23. Projectiles at an Angle  We will continue using the concepts we have already learned. 1.Separate velocity into horizontal and vertical components. 2.Use the motion equations to find the hang time, maximum height, and horizontal distance.

24. Projectiles at an Angle  Big Ideas:  Vertical velocity – accelerates due to gravity (9.8m/s 2 )  Horizontal velocity – remains constant  When finding the time it takes to reach the maximum height, remember to double it for the entire hang time.  Vertical velocity at the max height will be O for an instant.  Velocity upon reaching the same height the projectile was launched from will be the original velocity.

25. Projectiles at an Angle

26. Try It!  A discus is released at an angle of 45 degrees and a velocity of 24.0m/s.  How long does it stay in the air?  What horizontal distance does it travel?