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 x1 '(the x-pos of (the origin of ?the-component))) (:pair x2 '(the x-pos of (the destination of ?the-component))) (:pair dy '(the y-distance of ?the-component)) (:pair y1 '(the y-pos of (the origin of ?the-component))) (:pair y2 '(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 (- x2 x1))) '(= dx (* 0.5 (* ax (* t t)))) '(= dy (abs (- y2 y1))) '(= 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 CPLCPL> 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: _Duration1914

(_Duration1914 duration-of _Fall1901)

(_Duration1914 instance-of Thing) ; instance-of Duration-Value from range of duration-of

(_What1913 instance-of What) ; what?

(_X1910 value (:pair 125 *M))

(_X1910 height-of _Cliff1902)

(_X1910 instance-of Thing) ; instance-of Height-Value from range of height-of

(_Fall1901 duration _Duration1914)

(_Fall1901 destination _Ground1905)

(_Fall1901 origin _Top1904)

(_Fall1901 agent _Object1903) ; should be object (valid alternation for Move verbs with no dobj)

(_Fall1901 instance-of Fall)

(_Ground1905 destination-of _Fall1901) ; ground indirect anaphora (bottom part of cliff); bottom = 0 height

(_Ground1905 instance-of Ground)

(_Top1904 origin-of _Fall1901)

(_Top1904 is-part-of _Cliff1902)

(_Top1904 instance-of Cover) ; Cover is wrong sense of "top"; see new space ontology

(_Cliff1902 height _X1910)

(_Cliff1902 has-part _Top1904)

(_Cliff1902 instance-of Cliff)

(_Object1903 agent-of _Fall1901) ; should be object (see above)

(_Object1903 instance-of Substance) ; just bizarre

Revised Question FormulationCPL> An object falls from the top of a cliff to the ground.CPL> The initial horizontal velocity is 20 m/s.CPL> The height of the cliff is 125 m.CPL> What is the duration of the fall?

Query to find: (the duration of _Fall6)

(_Fall6 duration _Duration-Value5)(_Fall6 destination *Ground)(_Fall6 origin _Top11)(_Fall6 object _Physical-Object12)(_Fall6 instance-of Fall)(_Duration-Value5 instance-of Duration-Value) (_Height-Value7 value (:pair 125 *meter))(_Velocity-Value8 instance-of Velocity-Value)(_Velocity-Value8 value (:pair 20 *meter-per-second))(_Fall6 initial-x-velocity _Velocity-Value8)(_Cliff10 height _Height-Value7)(_Height-Value7 instance-of Height-Value)(_Cliff10 has-part _Top11)(_Top11 instance-of Top)(_Cliff10 instance-of Cliff)(_Physical-Object12 instance-of Physical-Object)

Model Instantiation_Fall6

duration: _Duration-Value5destination: *Groundorigin: _Top11object: _Physical-Object12initial-x-velocity: _Velocity-Value8

_Height-Value7value: (:pair 125 *meter)

_Velocity-Value8value: (:pair 20 *meter-per-second)

_Cliff10height: _Height-Value7has-part: _Top11

(a Fall-From-Rest with (x-acceleration ( (a Acceleration-Value with (value ((:pair 0 *m-per-s2)))))) (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))))

(a Viewpoint with (viewpoint-source (_Fall6)) (viewpoint-target ((a Fall-From-Rest-Model))) (viewpoint-correspondence ( (:pair . .) (:pair . .) (:pair . .) )))

Scenario: (the duration of _Fall6) Model Component:

Viewpoint:

Trace1. Solve A for t

A1 (= t (/ vy g))

2. Solve D for vyD1 (= vy (sqrt (- (* v v) (* vx vx)))) ; total-velocity unknown

3. No way in current equation set to find v

4. Solve B for tB1 (= t (/ x vx)) ; x-distance unknown

5. No way in current equation set to find x

6. Solve C for tC1 (= 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

A (= vy (* g t))B (= x (* vx t))C (= y (* (* 0.5 g) (* t t)))D (= v (sqrt (+ (* vx vx) (* vy vy))))

We'll show a new scenario with y-distance (y) as the query variable

Model Instantiation_Fall6

duration: _Duration-Value5destination: *Groundorigin: _Top11object: _Physical-Object12initial-x-velocity: _Velocity-Value8

_Height-Value7value: (:pair 125 *meter)

_Velocity-Value8value: (:pair 20 *meter-per-second)

_Cliff10height: _Height-Value9has-part: _Top11

(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))))

(a Viewpoint with (viewpoint-source (_Fall6)) (viewpoint-target ((a Move-Model))) (viewpoint-correspondence ( (:pair . .) (:pair . .) (:pair . .) (:pair . .) (:pair . .) )))

Scenario: (the y-distance of _Fall6)Model Component:

Viewpoint:

Trace1. Clone the scenario with dy = y

as the query variable

2. Solve G for dyG (= dy (abs (- y2 y1))) (= dy (abs (- 0m 125m))) (= dy (abs -125m)) (= dy 125m)

3. Subscenario "solved" ; y-distance now known

4. Revisit 6. (Solve C for t)C1 (= t (sqrt (/ y (* 0.5 g)))) (= t (sqrt (/ 125m (* 0.5 9.8m/s2)))) (= t (sqrt (/ 125m 4.9m/s2))) (= t (sqrt 25.5s2)) (= t 5.1s)

5. Scenario "solved" ; duration now known

E (= dx (abs (- x2 x1)))F (= dx (* 0.5 (* ax (* t t))))G (= dy (abs (- y2 y1))) H (= dy (* 0.5 (* ay (* t t))))I (= vx (* ax t)) J (= vy (* ay t)) K (= d (sqrt (+ (* dx dx) (* dy dy)))) L (= d (* 0.5 (* a (* t t)))) M (= v (sqrt (+ (* vx vx) (* vy vy))))

y1 is the y-pos of the origin of the Move,which is the Top has-part of the Cliff,which is equal to the height of the Cliff(minus the height of the Bottom has-partof the Cliff). See slide 1

Instantiated Scenario (Soln)_Fall6

duration: _Duration-Value5destination: *Groundorigin: _Top11object: _Physical-Object12initial-x-velocity: _Velocity-Value8y-distance: _Distance-Value13

_Height-Value7value: (:pair 125 *meter)

_Velocity-Value8value: (:pair 20 *meter-per-second)

_Cliff10height: _Height-Value9has-part: _Top11

_Duration-Value5value: (:pair 5.1 *second)

_Top11y-pos: (:pair 125 *meter)

*Groundy-pos: (:pair 0 *meter)

_Distance-Value13value: (:pair 125 *meter)