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.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
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) 2 4 6 8 10 (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
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.
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 0 2 + 2aΔx 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 0 2 + 2aΔx vx = v x0 + ax Δx = vx0 + ½ ax 2 vx 2 = vx0 2 + 2axΔx vy = v y0 + ay Δy = vy0 + ½ ay 2 vy 2 = vy0 2 + 2ayΔy 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 0 2 + 2aΔx 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
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!
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