v x + v 0 x v y + a y + v 0 y + 2a y + v y Today: Projectile motion Soccer problem Firefighter example

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1 Thurs Sep 10 Assign 2 Friday SI Sessions: Moron 227 Mon 8:10-9:10 PM Tues 8:10-9:10 PM Thur 7:05-8:05 PM Read Read Draw/Image lay ou coordinae sysem Wha know? Don' know? Wan o know? Physical Processes? Laws? Condiions? Valid Relaionships/Formulas Solve Break problems ino componens Link wih ime v x = v 0 x x = x 0 + v 0 x Today: Projecile moion Soccer problem Firefigher example y = y 0 + v y v y = 1 ( 2 v + v ) 0 y y v y = v 0 y + a y y = y 0 + v 0 y a y 2 v 2 y = v 2 0 y + 2a y (y y 0 ) hp://capa2.phy.ohiou.edu/res/ohiou/physles/2dkinemaics/proj2.hml

2 Adding 2 Vecors Graphically - Lab A B A R B A Tail-o-head mehod R is Resulan he resul of adding a group of vecors Parallelogram mehod works for 2 vecors Creae parallelogram ou of wo vecors Vecor from he wo ails o he opposie corner is he resulan A R B

3 Lab Nex Week: Forces and Equilibrium Equilibrium: forces balanced, acceleraion = 0 If a=0, forces are balanced Weigh: Force due o graviy: F g = mass*g Balance forces: boh in x and y

4 Definiions: Average velociy & acceleraion Chaper 3

5 Consan Acceleraion in 2 Dimensions If acceleraion consan: 2 ses of equaions for horizonal and verical moion x = x 0 + v x y = y 0 + v y g= 9.8 m/s 2 downward v x = 1 ( 2 v + v 0 x x) v x = v 0 x + a x v y = 1 ( 2 v + v ) 0 y y v y = v 0 y + a y x = x 0 + v 0 x a x 2 y = y 0 + v 0 y a y 2 v 2 x = v 2 0 x + 2a x (x x 0 ) v 2 y = v 2 oy + 2a y (y y 0 )

6 Projecile Moion If free-fall, acceleraion 9.8 m/s 2 downward AND If choose y-axis verical (+y up ypically) a x = 0 m/s 2, a y = 9.8 m/s 2 downward hp://capa2.phy.ohiou.edu/res/ohiou/physles/2dkinemaics/proj2.hml hps://phe.colorado.edu/en/simulaion/projecile-moion x = x 0 + v x v x = 1 ( 2 v + v 0 x x) v x = v 0 x + a x v x = v 0 x x = x 0 + v 0 x y = y 0 + v y v y = 1 ( 2 v + v ) 0 y y v y = v 0 y + a y x = x 0 + v 0 x a x 2 v 2 x = v 2 0 x + 2a x (x x 0 ) y = y 0 + v 0 y a y 2 v 2 y = v 2 0 y + 2a y (y y 0 )

7 "Reading he Problem" Verbal and visual clues Common heme: How do I find exra informaion when I don' hink I have enough? How do I know wha informaion refers o wha variable? - Speed refers o magniude of velociy (v). - Look for clues like 'horizonal/verical', look a drawing, look a pah. - If bulle leaving a horizonal gun barrel, wha's he iniial verical componen of he velociy? - Be careful no o assume hings you can : remember jus afer leaves, jus before his As soon as exra force, acceleraion no longer 9.8 m/s 2

v x0, v y0, a x, a y? v x0 = 4 m/s v y0 = 0 m/s a x = 0 m/s 2 a y = 9.

8 Waer Tank Waer leaves he ank raveling horizonally a a speed of 4 m/s. The spigo is 1 m above he ground. Wha are he values for he following quaniies? v x0, v y0, a x, a y? v x0 = 4 m/s v y0 = 0 m/s a x = 0 m/s 2 a y = 9.8 m/s 2 downward (which in his case is negaive) How much ime o hi ground? Ignore horizonal componens y = y 0 + v 0 y a y 2 1.0m = (0m/s) ( 9.8m/s2 ) 2

9 Example: Soccer Ball hp://capa2.phy.ohiou.edu/res/ohiou/physles/2dkinemaics/proj2.hml A soccer ball is kicked on a level playing field. I's iniial velociy is 20.0 m/s a an angle of 30 above he horizonal. Wha is he maximum heigh he ball reaches? How much ime is he ball in he air? Wha is he final speed of he ball jus before i his he ground? How far away does i hi he ground? (wha is he range) v x = v 0 x x = x 0 + v 0 x! Sec 3.3 v y = v 0 y + a y y = y 0 + v 0 y a y 2 y = y ( 2 v + v 0 y y) v 2 y = v 2 0 y + 2a y (y y 0 )

10 A soccer ball is kicked on a level playing field. I's iniial velociy is 20.0 m/s a an angle of 30 above he horizonal. Wha is he maximum heigh he ball reaches? (1) Drawing +y +x (3) Iniial/Final Iniial: jus afer ball leaves foo Final: ball a max heigh x=0,y=0 (2) Axes and origin (4) Known/Unknown Spli ino Horizonal and Verical x=? v x0 = 20 m/s cos(30º) = 17.3 m/s a x = 0 m/s 2 =? y =? v y0 = 20 m/s sin(30º) = +10m/s v y = 0 m/s a y = 9.8 m/s 2 down = -9.8 m/s 2 (5) Cons accel: Solve v 2 y = v 2 y0 + 2a y y 0 2 = (10 m/s) 2 + 2(-9.8 m/s 2 )y y = 5.1m

11 Soccer Ball: How much ime is he ball in he air? How far away does i hi he ground? Same drawing and coordinae sysem as las par (3) Iniial/Final Iniial: jus afer ball leaves foo Final: jus before his ground (4) Known/Unknown Spli ino Horizonal and Verical x=? v x0 = 20m/s cos(30º) = 17.3m/s a x = 0 m/s 2 =? y = 0 m v y0 = 20m/s sin(30º) = +10m/s v y =? a y = 9.8 m/s 2 down = -9.8 m/s 2 (5) Cons accel: Solve y = v y0 + ½a y 2 0 = (10m/s) +½ (-9.8m/s 2 ) 2 0 = (10m/s 4.9) = 0 or 2.04s x = v x0 = 17.3m/s (2.04s) = 35.3 m

12 Soccer Ball: Wha is he final speed of he ball jus before i his he ground? Same drawing and coordinae sysem as las par (3) Iniial/Final Iniial: jus afer ball leaves foo Final: jus before his ground (4) Known/Unknown Spli ino Horizonal and Verical x=? v x0 = 20m/s cos(30º) = 17.3m/s a x = 0 m/s 2 10m/s 17.3m/s θ =? v y = 0 m v y0 = 20m/s sin(30º) = +10m/s v y =? a y = 9.8 m/s 2 down = -9.8 m/s = v x + vy = (5) Cons accel: Solve To find magniude of velociy, need v x and v y v x = v x0 = 17.3 m/s v y = v y0 + a y v y = 10m/s + (-9.8m/s 2 )(2.04s) v y = -10 m/s = 20m/s θ = an -1 (10/17.3) = 30º below horizonal

13 A firefigher is spraying waer on a building. Waer leaves he hose a 35 m/s and an angle of 30 above he horizonal. The nozzle of he hose is 1.0 m above he ground, and he building is 22 m away. The building is 40 m all. Wha are he horizonal (x) and verical (y) componens of he iniial velociy (jus afer he waer leaves he hose)? (1) v x0 = 30.3 m/s; v y0 = 30.3 m/s (2) v x0 = 17.5 m/s; v y0 = 17.5 m/s (3) v x0 = 17.5 m/s; v y0 = 30.3 m/s (4) v x0 = 30.3 m/s; v y0 = 17.5 m/s (5) v x0 = 35.0 m/s; v y0 = 17.5 m/s (6) v x0 = 35.0 m/s; v y0 = 35.0 m/s 35 m/s 30º 35.0 cos(30º) = 30.3 m/s 35.0 sin(30º) = 17.5 m/s

14 A firefigher is spraying waer on a building. Waer leaves he hose a 35 m/s and an angle of 30 above he horizonal. The nozzle of he hose is 1.0 m above he ground, and he building is 22 m away. The building is 40 m all. How much ime does i ake for he waer o reach he building? (1) 0.63s (2) 0.73s (3) 1.00s (4) 1.32s (5) 1.78s You have enough informaion o deermine his from he horizonal par of he problem: You know v x =35*cos30 and ha he waer ravels 22 m

15 A firefigher is spraying waer on a building. Waer leaves he hose a 35m/s and an angle of 30 above he horizonal. The nozzle of he hose is 1.0m above he ground, and he building is 22m away. The building is 40m all. In wha verical direcion is he waer raveling when i his he building? (1) up (2) level (3) down Find v y a =0.72 s. If i is posiive, waer raveling up. If negaive, waer raveling down. v y = v y0 + a = 35*sin(30) + (-9.8)*0.72s = m/s Upward

16 A firefigher is spraying waer on a building. Waer leaves he hose a 35m/s and an angle of 30 above he horizonal. The nozzle of he hose is 1.0m above he ground, and he building is 22m away. The building is 40m all. Wha is he speed of he waer jus before i his he building? (1) 17.5 m/s (2) 30.3 m/s (3) 32.0 m/s (4) 35.0 m/s (5) 47.8 m/s Need x and y componens of speed. v x = 35*cos(30)=30.31 m/s v y jus found as 10.4 m/s Use Pyhagorean's heorem o find speed: 32.0 m/s

17 Velociy and Speed 17.5 m/s 35 m/s 30º 30.3 m/s Speed is magniude (size) of velociy vecor. Here i is 35 m/s Velociy would be 35 m/s 30º above he horizonal Verical componen of velociy would be m/s Horizonal componen of velociy would be m/s If you need he speed, you probably need o find he wo componens and reconsruc i A he beginning of he problem, you'll likely have o break he velociy ino componens.

18 Three projeciles are launched as described. Which one reaches he highes aliude? 1. A 5 kg ball launched sraigh up a 20 m/s 2. A 4 kg ball launched a 24 m/s a an angle 70 above he horizonal 3. A 2 kg ball launched a 27 m/s a an angle 50 above he horizonal 4. All hree reach he same maximum aliude Compare verical componens of velociy. Larges v y will go he highes.

19 A waer balloon is launched a a speed of 11 m/s from ground level a an angle of 50 degrees above he horizonal. The waer balloon is launched oward an innocen bysander who is 1.5 m all and sanding 2 m away. a) By how much does he waer balloon clear he person's head? b) How all can a person be and sill have he balloon clear? c) Wha is he alles a person can be and sill have he balloon clear if hey can sand where ever hey wan? d) How fas is he balloon raveling when i is direcly over he person's head in par (a)? (a) 0.49 m (b) 1.99 m (c) 3.63 m (d) 9.06m/s

20 Suden A is hanging from a ree. Suden B is on a local hillside aiming a waer balloon direcly horizonally a Suden A. Suden B les ou a loud scream and releases he waer balloon. Suden A les go of he branch a he same ime he waer balloon is released. The waer balloon will: 1. pass above Suden A 2. hi Suden A 3. pass below Suden A Boh suden and waer balloon have an iniial velociy of zero and fall a same rae.

21 Ho Wheels on Coffee Table Ryan pushes his Ho Wheels car horizonally off he coffee able wih jus he righ speed o sick i in beween he cushions on our living room chair. The chair is 0.35 m from he edge of he able. The crack beween he cushions is 0.05 m below he level of he coffee able. 1. How much ime is he car in free fall? 2. How fas mus he push he car o hi he middle of he crack?

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile