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# 2.3 010 projectile_motion

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### 2.3 010 projectile_motion

1. 1. How does the horizontal and vertical motion differ on the x- and y-planes?
2. 2. Horizontally…
3. 3. Vertically…
4. 4. Combined…
5. 5. Combined…
6. 6. Actual…
7. 7. Motion Diagrams
8. 8. Projectile Motion For a projectile: a) b) c) Describe the horizontal and vertical motion. Horizontal constant velocity Vertical accelerating Describe the horizontal and vertical Horizontal zero acceleration. Vertical 9.8 m/s2 What equations would you use to calculate horizontal and vertical motion. Horizontal v = d/t Vertical v = at and d = ½ at2
9. 9. Horizontally… If you throw a projectile horizontally Describe the horizontal will it What is the horizontal at a speed of 25 m/s, how fast acceleration for projectile. 3 s? motion of a a projectile? be moving, horizontally, after A projectile moveswill still be Horizontally, it horizontally Horizontal acceleration is zero. with constant25 m/s. moving at velocity.
10. 10. If a projectile is thrown What What a speed horizontally at happens, vertically, as a happens, vertically, as of 25 m/s, howvertical Describe the fast is aprojectile moves projectile moves the projectile moving motion of a projectile. upward? 3 downward? s? vertically after Vertically, a projectile slows Vertically, a projectile speeds Vertically, projectile will a way up. Vertically,on the projectile theway down. down the up on accelerates… be moving 29.4 m/s. …at a rate of 9.8 m/s2 Vertically…
11. 11. Initially… 25 m/s 0 vertical velocity So, if you throw a projectile horizontally at a speed of After 3 s… 25 m/s 25 m/s, how fast is it moving after 3 seconds? actual 30 m/s Horizontally, it is moving at 25 39 m/s m/s, vertically it is moving 30 30 m/s m/s, so (by Pythagorean’s Theorem) the projectile is moving 25 m/s at 39 m/s. motion
12. 12. Group 1 2 3 4 5 6 7 8 9 10 Round 1 Round 2 Round 3
13. 13. B4 stopped Projectile motion problems… The key to solving problems involving projectile motion is… • understanding that x and y are independent. • identifying and separating x and y variables. • understanding that time is the same for both x and y. • Using appropriate equations for x and y.
14. 14. Projectile motion problems… Useful tips… • Draw a picture. • Make a table with an x column and a y column to identify variables. • Immediately write down acceleration due to gravity (g) in the y column. • Time connects x and y.
15. 15. Projectile motion problems… Equations… • Along the x-axis: – no acceleration; moves w/ constant velocity. – v = d/t • Along the y-axis: – Accelerates b/c of gravity; g = 9.8 m/s2. – v = at – d = ½at2
16. 16. Lamp on a table… If I knock a lamp off an end-table with a horizontal velocity of 5 m/s and the table is 0.5 meters high, how far away does the lamp land? 1.6 meters in front of table.
17. 17. B1 stopped Kickin’ rocks… A rock is kicked horizontally off a cliff and lands 125 meters in front of the cliff. If the cliff is 80 meters high, how fast is the rock initially kicked? 31.25 m/s horizontally.
18. 18. A2 stopped Tossing pennies… A penny is thrown horizontally of a building with a velocity of 10 m/s. If the penny lands 78 meters in front of the building, how tall is the building? It is 304.2 meters tall.
19. 19. Stranded on a mountain… An airplane traveling at 80 m/s at an elevation of 250 m, drops a box of supplies to skiers stranded in a snowstorm. At what horizontal distance from the skiers should the supplies be dropped? They need to be dropped 571.43 m before target (565.69 if using 10).
20. 20. Stranded on a mountain… (con’t) What is the speed of the box as it reaches the ground? It is going 106.3 m/s (106.8 m/s if using 10)
21. 21. Stone throw… Paco, standing on a cliff, throws a stone with a horizontal velocity of 15.0 m/s and the stone hits the ground 47.0 m from the base of the cliff. How high is the cliff? The cliff is 48 m high.