1. A projectile is any object in free fall –Gravity is the only influence! –Ignore Air Resistance –Vertical Velocity Changes 1

2. Vertical!!! Final Velocity is 0 m/sec at maximum height The time to go up is equal to the time to come back down! Final Velocity is opposite of initial when it returns to initial position on a round trip. 2

3. Horizontal!!!!! –Sometimes, it goes horizontally AS WELL AS up & down –Since gravity is only downward, it does not effect horizontal motion –Horizontal Velocity is CONSTANT!!!!!!! 3

4. Remember that a dropped object (or any object in free fall, for that matter) falls a certain distance after a certain time. Use this modified equation: tyfyf 1 s-5 m 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s tyfyf 1 s-5 m 2 s-20 m 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s tyfyf 1 s-5 m 2 s-20 m 3 s-45 m 4 s 5 s 6 s 7 s 8 s 9 s 10 s tyfyf 1 s-5 m 2 s-20 m 3 s-45 m 4 s-80 m 5 s 6 s 7 s 8 s 9 s 10 s tyfyf 1 s-5 m 2 s-20 m 3 s-45 m 4 s-80 m 5 s-125 m 6 s 7 s 8 s 9 s 10 s tyfyf 1 s-5 m 2 s-20 m 3 s-45 m 4 s-80 m 5 s-125 m 6 s-180 m 7 s 8 s 9 s 10 s tyfyf 1 s-5 m 2 s-20 m 3 s-45 m 4 s-80 m 5 s-125 m 6 s-180 m 7 s-245 m 8 s 9 s 10 s tyfyf 1 s-5 m 2 s-20 m 3 s-45 m 4 s-80 m 5 s-125 m 6 s-180 m 7 s-245 m 8 s-320 m 9 s 10 s tyfyf 1 s-5 m 2 s-20 m 3 s-45 m 4 s-80 m 5 s-125 m 6 s-180 m 7 s-245 m 8 s-320 m 9 s-405 m 10 s tyfyf 1 s-5 m 2 s-20 m 3 s-45 m 4 s-80 m 5 s-125 m 6 s-180 m 7 s-245 m 8 s-320 m 9 s-405 m 10 s-500 m 4

5. Each square = 20 m 5 5m 20m 45m 125m 80m 180m 0 sec 1 sec 2 sec 3 sec 4 sec 5 sec 6 sec

6. Each square = 20 m 6 0 1 sec 2 sec 3 sec 4 sec 5 sec 6 sec 5m 20m 45m 80m 125m 180m

7. Each square = 20 m 7

8. 8 Cliffhangers are projectiles that are moving horizontally WHILE being dropped! Remember: The Horizontal Velocity (v x ) is CONSTANT! The Vertical Velocity is Changing (speeding up) Cliffhangers!

9. CliffHanger Problems Now you have 2 sets of givens: But you know they occur at the SAME TIME, so TIME – and only TIME – can be used for both columns!!!! Horizontal is constant! So you’ll only have d, v x, & t. Vertical has g, and for a CliffHanger, v iy = 0 m/sec Toss-Up Problems No horizontal- just Up & Down! Tricky because the object lands below its starting point ( is negative) Initial Velocity (v iy ) is NOT equal to Final Velocity (v fy ) – not a round trip! Easiest way to solve for time: Factoring (unFOIL)! 9 HorizontalVertical yiyi yfyf

10. Foil review g rrrrr algebra * Please write on separate sheet of paper In order to do some of these we have to go backwards! “un-FOIL” You will get two answers you MUST choose wisely

11. 2. Measure the angle- that is the “Intended Path” of the projectile, if there was no gravity 11 1. Make a motion map of the HORIZONTAL component of velocity (which is given) 3. Plot the position points along that “intended path” 4. Use your Magic Numbers to plot the actual position points of the projectile

12. Doing the Diagonal Launch Problems 1. Make a motion map of the HORIZONTAL component of velocity (which is given) 2. Measure the angle- that is the “Intended Path” of the projectile, if there was no gravity 3. Plot the position points along that “intended path” go to each point on the horizontal path, and go up (or down) until you get to the diagonal line! 4. Use your Magic Numbers to plot the actual position points of the projectile 12

13. 13

14. TimeYfYf

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