Physics Question 1 From AP Physics Syllabus Examples
Physics Question 1 [From AP Physics Syllabus Examples] 1. An object is thrown with a horizontal velocity of 20 m/s from a cliff that is 125 m above level ground. If air resistance is negligible, the time that it takes the object to fall to the ground from the cliff is most nearly (a) 3 s (b) 5 s (c) 6 s etc.
CLib (*Gravity has (instance-of (Acceleration-Value)) (value ((: pair 9. 8 *meter-per-second-squared)))) (every Physical-Object has (height ( ((a Height-Value with (value ((the y-pos of (the Top has-part of Self))))) property-minus (a Height-Value with (value ((the y-pos of (the Bottom has-part of Self))))) (has-part ((a Top with (y-pos (. . . ))))) (has-part ((a Bottom with (y-pos (. . . ))))) (width (. . . )) )
CLib (Move has (superclasses (Action))) (every Move has (object ((a Physical-Object with (mass ((a Mass-Value))) (possesses ((a Kinetic-Energy)))))) (origin ((a Spatial-Entity with (x-pos (. . . ))) (destination ((a Spatial-Entity with (x-pos (. . . ))) (x-acceleration ((a Acceleration-Value))) (y-acceleration ((a Acceleration-Value))) (total-acceleration ((a Acceleration-Value))) (x-velocity ((a Velocity-Value))) (y-velocity ((a Velocity-Value))) (total-velocity ((a Velocity-Value))) (x-distance ((a Distance-Value))) (y-distance ((a Distance-Value))) (total-distance ((a Distance-Value))) (duration ((a Duration-Value))) )
Move-Model. km (Move-Model has (superclasses (Model))) (every Move-Model has (model-component ((a Move))) (model-equation-set ((a Move-Equation-Set))) (model-lexicon ( (: pair "time" '(the duration of (the model-component of Self))))) )
Move-Equation-Set. km (Move-Equation-Set has (superclasses (Equation-Set))) (every Move-Equation-Set has (model-symbols (( (? the-component == (the model-component of (the model-equation-set-of of Self))) and (: set (: pair t '(the duration of ? the-component)) (: pair ax '(the x-acceleration of ? the-component)) (: pair ay '(the y-acceleration of ? the-component)) (: pair a '(the total-acceleration of ? the-component)) (: pair vx '(the x-velocity of ? the-component)) (: pair vy '(the y-velocity of ? the-component)) (: pair v '(the total-velocity of ? the-component)) (: pair dx '(the x-distance of ? the-component)) (: pair x 1 '(the x-pos of (the origin of ? the-component))) (: pair x 2 '(the x-pos of (the destination of ? the-component))) (: pair dy '(the y-distance of ? the-component)) (: pair y 1 '(the y-pos of (the origin of ? the-component))) (: pair y 2 '(the y-pos of (the destination of ? the-component))) (: pair d '(the total-distance of ? the-component)) )))) (model-equations (. . . )) )
Move-Equation-Set. km (Move-Equation-Set has (superclasses (Equation-Set))) (every Move-Equation-Set has (model-symbols (. . . )) (model-equations (('(= dx (abs (- x 2 x 1))) '(= dx (* 0. 5 (* ax (* t t)))) '(= dy (abs (- y 2 y 1))) '(= dy (* 0. 5 (* ay (* t t)))) '(= vx (* ax t)) '(= vy (* ay t)) '(= d (sqrt (+ (* dx dx) (* dy dy)))) '(= d (* 0. 5 (* a (* t t)))) '(= v (sqrt (+ (* vx vx) (* vy vy)))) )
Fall-From-Rest. km (Fall-From-Rest has (superclasses (Fall))) (every Fall-From-Rest has (x-acceleration ((a Acceleration-Value with (value ((: pair 0 *meter-per-second-squared)))))) (y-acceleration (*Gravity)) (object ((a Physical-Object))) (x-velocity ((a Velocity-Value))) ; differs from Novak (y-velocity ((a Velocity-Value))) (x-distance ((a Distance-Value))) (y-distance ((a Distance-Value))) (total-velocity ((a Velocity-Value))) (duration ((a Duration-Value))) )
Fall-From-Rest-Model. km (Fall-From-Rest-Model has (superclasses (Model))) (every Fall-From-Rest-Model has (model-component ((a Fall-From-Rest))) (model-equation-set ((a Fall-From-Rest-Equation-Set))) (model-assumption ( (: triple (the object of (the model-component of Self)) acted-on-by-force (mustnt-be-a Friction-Force))) (: triple (the model-component of Self) initial-y-velocity (a Velocity-Value with (value ((: pair 0 *meter-per-second))))). . . )) (model-lexicon ( (: pair "height" '(the y-distance of (the model-component of Self))) (: pair "time" '(the duration of (the model-component of Self))))) )
Fall-From-Rest-Equation-Set. km (Fall-From-Rest-Equation-Set has (superclasses (Equation-Set))) (every Fall-From-Rest-Equation-Set has (model-symbols (( (? the-component == (the model-component of (the model-equation-set-of of Self))) and (: set (: pair t '(the duration of ? the-component)) (: pair g '(the y-acceleration of ? the-component)) (: pair vy '(the y-velocity of ? the-component)) (: pair vx '(the x-velocity of ? the-component)) (: pair x '(the x-distance of ? the-component)) (: pair y '(the y-distance of ? the-component)) (: pair v '(the total-velocity of ? the-component)) )))) (model-equations (('(= vy (* g t)) '(= x (* vx t)) '(= y (* (* 0. 5 g) (* t t))) '(= v (sqrt (+ (* vx vx) (* vy vy)))) )
Question Formulation from CPL> An object falls from the top of a cliff to the ground. CPL> The height of the cliff is 125 m. ; initial horizontal velocity missing? CPL> What is the duration of the fall? Query to find: _Duration 1914 (_Duration 1914 duration-of _Fall 1901) (_Duration 1914 instance-of Thing) ; instance-of Duration-Value from range of duration-of (_What 1913 instance-of What) ; what? (_X 1910 value (: pair 125 *M)) (_X 1910 height-of _Cliff 1902) (_X 1910 instance-of Thing) ; instance-of Height-Value from range of height-of (_Fall 1901 duration _Duration 1914) (_Fall 1901 destination _Ground 1905) (_Fall 1901 origin _Top 1904) (_Fall 1901 agent _Object 1903) ; should be object (valid alternation for Move verbs with no dobj) (_Fall 1901 instance-of Fall) (_Ground 1905 destination-of _Fall 1901) ; ground indirect anaphora (bottom part of cliff); bottom = 0 height (_Ground 1905 instance-of Ground) (_Top 1904 origin-of _Fall 1901) (_Top 1904 is-part-of _Cliff 1902) (_Top 1904 instance-of Cover) ; Cover is wrong sense of "top"; see new space ontology (_Cliff 1902 height _X 1910) (_Cliff 1902 has-part _Top 1904) (_Cliff 1902 instance-of Cliff) (_Object 1903 agent-of _Fall 1901) ; should be object (see above) (_Object 1903 instance-of Substance) ; just bizarre
Revised Question Formulation CPL> An object falls from the top of a cliff to the ground. The initial horizontal velocity is 20 m/s. The height of the cliff is 125 m. What is the duration of the fall? Query to find: (the duration of _Fall 6) (_Fall 6 duration _Duration-Value 5) (_Fall 6 destination *Ground) (_Fall 6 origin _Top 11) (_Fall 6 object _Physical-Object 12) (_Fall 6 instance-of Fall) (_Duration-Value 5 instance-of Duration-Value) (_Height-Value 7 value (: pair 125 *meter)) (_Velocity-Value 8 instance-of Velocity-Value) (_Velocity-Value 8 value (: pair 20 *meter-per-second)) (_Fall 6 initial-x-velocity _Velocity-Value 8) (_Cliff 10 height _Height-Value 7) (_Height-Value 7 instance-of Height-Value) (_Cliff 10 has-part _Top 11) (_Top 11 instance-of Top) (_Cliff 10 instance-of Cliff) (_Physical-Object 12 instance-of Physical-Object)
Model Instantiation Scenario: (the duration of _Fall 6) Model Component: _Fall 6 duration: _Duration-Value 5 destination: *Ground origin: _Top 11 object: _Physical-Object 12 initial-x-velocity: _Velocity-Value 8 _Height-Value 7 value: (: pair 125 *meter) _Velocity-Value 8 value: (: pair 20 *meter-per-second) _Cliff 10 height: _Height-Value 7 has-part: _Top 11 Viewpoint: (a Fall-From-Rest with (x-acceleration ( (a Acceleration-Value with (value ((: pair 0 *m-per-s 2)))))) (y-acceleration (*Gravity)) (object ((a Physical-Object))) (x-velocity ((a Velocity-Value))) (y-velocity ((a Velocity-Value))) (x-distance ((a Distance-Value))) (y-distance ((a Distance-Value))) (total-velocity ((a Velocity-Value))) (duration ((a Duration-Value))) )
Trace 1. Solve A for t A 1 (= t (/ vy g)) 2. Solve D for vy D 1 (= vy (sqrt (- (* v v) (* vx vx)))) ; total-velocity unknown 3. No way in current equation set to find v 4. Solve B for t B 1 (= t (/ x vx)) ; x-distance unknown 5. No way in current equation set to find x 6. Solve C for t C 1 (= t (sqrt (/ y (* 0. 5 g)))) ; y-distance unknown 7. No way in current equation set to find y 8. Impasse: need to import another model 9. Clone the scenario with v, x or y as the query variable and choose a new model
Model Instantiation Scenario: (the y-distance of _Fall 6) Model Component: _Fall 6 duration: _Duration-Value 5 destination: *Ground origin: _Top 11 object: _Physical-Object 12 initial-x-velocity: _Velocity. Value 8 _Height-Value 7 value: (: pair 125 *meter) _Velocity-Value 8 value: (: pair 20 *meter-per-second) _Cliff 10 height: _Height-Value 9 has-part: _Top 11 Viewpoint: (a Move with (object ( (a Physical-Object with (mass ((a Mass-Value))) (possesses ((a Kinetic-Energy)))))) (origin ((a Spatial-Entity))) (destination ((a Spatial-Entity))) (x-acceleration ((a Acceleration-Value))) (y-acceleration ((a Acceleration-Value))) (total-acceleration ((a Acceleration-Value))) (x-velocity ((a Velocity-Value))) (y-velocity ((a Velocity-Value))) (total-velocity ((a Velocity-Value))) (x-distance ((a Distance-Value))) (y-distance ((a Distance-Value))) (total-distance ((a Distance-Value))) (duration ((a Duration-Value))) )
Trace 1. Clone the scenario with dy = y as the query variable 2. Solve G for dy G (= dy (abs (- y 2 y 1))) (= dy (abs (- 0 m 125 m))) (= dy (abs -125 m)) (= dy 125 m) 3. Subscenario "solved" ; y-distance now known 4. Revisit 6. (Solve C for t) C 1 (= t (sqrt (/ y (* 0. 5 g)))) (= t (sqrt (/ 125 m (* 0. 5 9. 8 m/s 2)))) (= t (sqrt (/ 125 m 4. 9 m/s 2))) (= t (sqrt 25. 5 s 2)) (= t 5. 1 s) 5. Scenario "solved" ; duration now known
Instantiated Scenario _Fall 6 duration: _Duration-Value 5 destination: *Ground origin: _Top 11 object: _Physical-Object 12 initial-x-velocity: _Velocity-Value 8 y-distance: _Distance-Value 13 _Height-Value 7 value: (: pair 125 *meter) _Velocity-Value 8 value: (: pair 20 *meter-per-second) _Cliff 10 height: _Height-Value 9 has-part: _Top 11 _Duration-Value 5 value: (: pair 5. 1 *second) _Top 11 y-pos: (: pair 125 *meter) *Ground y-pos: (: pair 0 *meter) _Distance-Value 13 value: (: pair 125 *meter) n (Sol )
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