Guest Lecturer Friday! Symbolic reasoning. Symbolic reasoning. Practice Problem day A. 2 B. 3 C. 4 D. 8 E. 16 Q25. Will Armentrout.

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Pracice Problem day Gues Lecurer Friday! Will Armenrou. He d welcome your feedback! Anonymously: wrie somehing and pu i in my mailbox a 111 Whie Hall. Email me: sarah.spolaor@mail.wvu.

1 Pracice Problem day Gues Lecurer Friday! Will Armenrou. He d welcome your feedback! Anonymously: wrie somehing and pu i in my mailbox a 111 Whie Hall. me: sarah.spolaor@mail.wvu.edu Symbolic reasoning A woman measures he angle of elevaion of a mounainop. Suppose he mounain heigh is y, he woman's original disance from he mounain is x, and he angle of elevaion she measures from he horizonal o he op of he mounain is θ. If she moves a disance d closer o he mounain and measures an angle of elevaion ϕ, find a general equaion for he heigh of he mounain y in erms of d, ϕ, and θ, neglecing he heigh of her eyes above he ground. Symbolic reasoning If you oss a ball upward wih a cerain iniial speed, i falls freely and reaches a maximum heigh h. By wha facor mus you increase he iniial speed of he ball for i o reach a maximum heigh 4h? Jus because i s a concepual problem, doesn mean you can use numbers! A. 2 v = vo + a B. 3 Δx = vo + 12 a 2 C. 4 v 2 = vo 2 + 2aΔx D. 8 E. 16 Same syle as some concepual quesions on he es! Q25

2 Graphing again! Δx = 40m - 60m v = Δx = Δ xf - xi f - i Δ = 45s - 30s Wha s he average velociy beween 30 and 45 seconds? A. 1.3 m/s B. 13 m/s C. 15 m/s D. 20 m/s E. 102 m/s Q26 Graphing again! v (m/s) (m/s) Wha s he insananeous acceleraion a poin B? A. 1.3 m/s 2 B. 15 m/s 2 C. 20 m/s 2 D. 30 m/s 2 E. 0 m/s 2 Q27 Cha abou he moion in each of hese graphs. Wha s happening o he moving objec? Are all of hese graph ses valid? A. B. C. D. No alking now please! Which se of graphs is NOT valid? A. B. C. D. Q28

3 Projecile moion A penguin runs horizonally off he op of an iceberg a 3 m/s and his he waer a a disance of 10m. How all is he iceberg? Does his problem require analysis of horizonal or verical movemen? A. Verical B. Horizonal C. Boh Q29 Remember! Trea X and Y movemens separaely unless asked for acual speed/velociy! (or oal velociy, ne velociy, magniude of velociy) Remember! The ime will be he same for x and y pars of he quesion. If you don have enough informaion for x or y componens, solve for ime and reassess wha you can deermine. Remember! Someimes i really helps o rewrie your moion equaions in erms of x and y componens.

4 A penguin runs horizonally off he op of an iceberg a 3 m/s and his he waer a a disance of 10m. How all is he iceberg? v = v 0 + a Δx = v 0 + ½ a 2 v 2 = v aΔx Try rewriing your equaions on he equaion shee before you do projecile moion problems! A penguin runs horizonally off he op of an iceberg a 3 m/s and his he waer a a disance of 10m. How all is he iceberg? v = v 0 + a Δx = v 0 + ½ a 2 v 2 = v aΔx vx = v x0 + ax Δx = vx0 + ½ ax 2 vx 2 = vx axΔx vy = v y0 + ay Δy = vy0 + ½ ay 2 vy 2 = vy ayΔy Try rewriing your equaions on he equaion shee before you do projecile moion problems! A penguin runs horizonally off he op of an iceberg a 3 m/s and his he waer a a disance of 10m. How all is he iceberg? ax = 0 m/s 2 ay = -g = -9.8 m/s 2* v = v 0 + a Δx = v 0 + ½ a 2 v 2 = v aΔx vx = v x0 Δx = vx0 vx 2 = vx0 2 vy = v y0 - g Δy = vy0 - ½ g 2 vy 2 = vy0 2-2gΔy * ONLY IF you define +y as up (like we usually do!) A penguin runs horizonally off he op of an iceberg a 3 m/s and his he waer a a disance of 10m. How all is he iceberg? vx = v x0 Δx = vx0 vx 2 = vx0 2 vy = v y0 - g Δy = vy0 - ½ g 2 vy 2 = vy0 2-2gΔy

5 A penguin runs horizonally off he op of an iceberg a 3 m/s and his he waer a a disance of 10m. How all is he iceberg? We don have enough info o solve for Δy! So solve for ime in he x-dimension. Now you can solve for Δy! Throwing somehing off of a cliff (5 examples wih increasing difficuly) A ball is launched from he edge of a 15.0m all cliff a 16 m/s a an angle of 60 degrees from he horizonal. Wha is he magniude of is velociy jus before i his he ground? Wha is he angle ha i his he ground from he horizonal? How do we ge is is final velociy vecor? Final angle: which way is he ball going? Throwing somehing off of a cliff (5 examples wih increasing difficuly) A ball is launched from he edge of a 15.0m all cliff a 16 m/s a an angle of 60 degrees from he horizonal. Wha is he magniude of is velociy jus before i his he ground? Wha is he angle ha i his he ground from he horizonal? How do we ge is is final velociy vecor? Final angle: which way is he ball going? vx = v x0 Δx = vx0 vx 2 = vx0 2 vy = v y0 - g Δy = vy0 - ½ g 2 vy 2 = vy0 2-2gΔy Magniude and Angle ha i his he ground? A ball is launched from he edge of a 15.0m all cliff a 16 m/s a an angle of 60 degrees from he horizonal. We need o solve for vx and vy o deermine he final velociy vecor. Once we know ha, we can calculae he angle and magniude of ha vecor. Tha represens he angle of impac of he ball. v x v y v Vecor sum!

6 Magniude and Angle ha i his he ground? A ball is launched from he edge of a 15.0m all cliff a 16 m/s a an angle of 60 degrees from he horizonal. Vecor sum! v x v y v 1. We know vx = vx0, so solve for vx0 2. How o ge final vy? a. Trea y dimension movemen independenly! b. We don have enough info a firs, bu we do see ha here are wo equaions wih wo unknowns (unknowns: vy and ime). c. Solve for ime using a moion equaion wih sufficien knowns: Δx = v 0 + ½ a 2 (or in erms of y dimension, we can rewrie his as Δy = vy0 - ½ g 2 ). d. Now we can solve eiher of he oher moion equaions (in verical direcion) for vy. 3. See nex slide for magniude and angle calculaion! Magniude and Angle ha i his he ground? A ball is launched from he edge of a 15.0m all cliff a 16 m/s a an angle of 60 degrees from he horizonal. c 2 = a 2 + b 2 = (8.0m/s) 2 + (-22m/s) 2 c = 23.4 m/s anθ = opp/adj = (-22 m/s) / (8m/s) Θ = an -1 (-22/8) = -70 The objec is moving a 23m/s a an angle of 70 below he horizonal when i his he ground. -22

Best test practice: Take the past test on the class website

Best test practice: Take the past test on the class website Bes es pracice: Take he pas es on he class websie hp://communiy.wvu.edu/~miholcomb/phys11.hml I have posed he key o he WebAssign pracice es. Newon Previous Tes is Online. Forma will be idenical. You migh