# Example 980 — The head on at fifty each hit like fifty not a hundred `the_head_on_at_fifty_each_hit_like_fifty_not_a_hundred.eml` - A road-safety talk describes two identical 1500 kg cars meeting head-on at 50 km/h each, adds the speeds to a closing speed of 100, and tells the audience that each driver takes the crash of hitting a wall at 100. What each car actually goes through, and when the closing speed does matter, is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). A road-safety talk # describes two identical 1500 kg cars meeting head-on at 50 km/h each, adds the # speeds to a closing speed of 100, and tells the audience that each driver # takes the crash of hitting a wall at 100. What each car actually goes through, # and when the closing speed does matter, is computed below. # # The reasoning is careful. Each car really is doing 50; the closing speed # really is 100; both cars really do stop dead in the crash; and the intent is # exactly 'how hard is this crash for each driver'. # # What a car's occupants go through is the car's own change of speed. Two equal # cars with equal and opposite momentum both end at rest, so each changes speed # by 50 - a wall at 50, a quarter of the energy of a wall at 100. The closing # speed matters only through the masses: a 1500 kg car meeting a 15000 kg truck # at the same 50 each changes speed by 90, while the truck changes by 9. 50 => each_car_kmh 1500 => car_kg 15000 => truck_kg 2 * each_car_kmh => closing_speed_kmh car_kg * each_car_kmh => momentum_eastbound car_kg * each_car_kmh => momentum_westbound momentum_eastbound - momentum_westbound => momentum_left_after_the_crash int(momentum_left_after_the_crash / (2 * car_kg)) => speed_after_the_crash_kmh each_car_kmh - speed_after_the_crash_kmh => each_cars_change_of_speed_kmh int(each_cars_change_of_speed_kmh * each_cars_change_of_speed_kmh * 1000 / (closing_speed_kmh * closing_speed_kmh)) => each_cars_energy_vs_a_wall_at_100_per_mille int(2 * each_car_kmh * truck_kg / (car_kg + truck_kg)) => car_change_of_speed_against_the_truck_kmh int(2 * each_car_kmh * car_kg / (car_kg + truck_kg)) => truck_change_of_speed_kmh int(truck_kg / car_kg) => truck_outweighs_the_car_by "each car : " + str(car_kg) + " kg at " + str(each_car_kmh) + " km/h" ^0 "closing speed : " + str(closing_speed_kmh) + " km/h" ^0 "momentum, one each way : " + str(momentum_eastbound) + " and " + str(momentum_westbound) + ", " + str(momentum_left_after_the_crash) + " left after the crash" ^0 "speed after the crash : " + str(speed_after_the_crash_kmh) + " km/h" ^0 "each car's change of speed : " + str(each_cars_change_of_speed_kmh) + " km/h, a wall at " + str(each_cars_change_of_speed_kmh) ^0 "each car's energy vs a wall at " + str(closing_speed_kmh) + " : " + str(each_cars_energy_vs_a_wall_at_100_per_mille) + " per mille" ^0 "" ^0 "a car against a truck : truck " + str(truck_kg) + " kg, " + str(truck_outweighs_the_car_by) + " times the car" ^0 " the car's change of speed : " + str(car_change_of_speed_against_the_truck_kmh) + " km/h" ^0 " the truck's change of speed : " + str(truck_change_of_speed_kmh) + " km/h" ^0 "" ^0 # ---- what the talk verified ---- "the add-the-speeds reasoning" ^0 " each car : " + str(each_car_kmh) + " km/h" ^0 " closing speed : " + str(closing_speed_kmh) + " km/h" ^0 " outcome : both cars stop dead" ^0 " intent : how hard is this crash for each driver" ^0 " facts wrong : 0" ^0 " verdict : EACH DRIVER HITS A WALL AT " + str(closing_speed_kmh) ^0 "" ^0 " adding the two speeds is the part done right here, and it is" ^0 " why the cars really do close on each other at " + str(closing_speed_kmh) + " km/h" ^0 "" ^0 # ---- what each car goes through ---- "the change of speed" ^0 " what the occupants feel : their own car's change of speed, over" ^0 " the time its front crumples" ^0 " two equal cars : equal and opposite momentum, " + str(momentum_left_after_the_crash) + " left, so both" ^0 " stop, and each changes speed by " + str(each_cars_change_of_speed_kmh) + " km/h" ^0 " a wall at " + str(closing_speed_kmh) + " : a change of " + str(closing_speed_kmh) + ", four times the energy; each" ^0 " car here takes " + str(each_cars_energy_vs_a_wall_at_100_per_mille) + " per mille of that" ^0 " when the closing speed bites : when the masses differ; the" ^0 " light car is flung backwards by the heavy one, a change of" ^0 " " + str(car_change_of_speed_against_the_truck_kmh) + " km/h against the truck's " + str(truck_change_of_speed_kmh) ^0 "" ^0 # ---- what the audience got ---- "the lesson" ^0 " believed : a head-on at " + str(each_car_kmh) + " each is a wall at " + str(closing_speed_kmh) ^0 " actual : for equal cars, a wall at " + str(each_cars_change_of_speed_kmh) + "; against a truck, nearly" ^0 " a wall at " + str(car_change_of_speed_against_the_truck_kmh) ^0 " is the closing speed wrong : no; it is " + str(closing_speed_kmh) ^0 " does the closing speed say what each car goes through : no;" ^0 " that depends on how the momentum is shared" ^0 "" ^0 # ---- null control ---- # The same crash read from each car's change of speed instead of from the # closing speed. 100 => nc_change_of_speed_read_from_the_closing_speed_kmh 50 => nc_change_of_speed_read_from_the_momentum_kmh 50 => nc_kmh_the_momentum_reading_removes "null control - read the crash from each car's change of speed" ^0 " change of speed, read from the closing speed : " + str(nc_change_of_speed_read_from_the_closing_speed_kmh) + " km/h" ^0 " change of speed, read from the momentum : " + str(nc_change_of_speed_read_from_the_momentum_kmh) + " km/h" ^0 " km/h the momentum reading removes : " + str(nc_kmh_the_momentum_reading_removes) ^0 " no car and no speed changed; each car was judged by what" ^0 " happened to it, not by the gap the two of them closed" ^0 "" ^0 # ---- the rule ---- "what a closing speed of " + str(closing_speed_kmh) + " guarantees" ^0 " the cars approach each other at " + str(closing_speed_kmh) + " : exactly" ^0 " each car crashes as if into a wall at " + str(closing_speed_kmh) + " : not addressed; with" ^0 " equal masses each car's speed changes by " + str(each_cars_change_of_speed_kmh) + ", a wall at " + str(each_cars_change_of_speed_kmh) + " and" ^0 " " + str(each_cars_energy_vs_a_wall_at_100_per_mille) + " per mille of the energy - and it is the mass ratio that" ^0 " decides, a change of " + str(car_change_of_speed_against_the_truck_kmh) + " for the car against a truck" ^0 "" ^0 "a closing speed describes the gap, not the people in it; what each of them" ^0 "goes through is their own change of speed, and that is shared out by mass" ^0 "" ^0 "The cars close at " + str(closing_speed_kmh) + " km/h - that is exact. But each car's occupants feel their" ^0 "own change of speed, and two equal cars both stop: a change of " + str(each_cars_change_of_speed_kmh) + ", a wall at" ^0 "" + str(each_cars_change_of_speed_kmh) + ", " + str(each_cars_energy_vs_a_wall_at_100_per_mille) + " per mille of the energy of one at " + str(closing_speed_kmh) + ", while the same car against a truck" ^0 "changes by " + str(car_change_of_speed_against_the_truck_kmh) + ", until the crash is read by what happens to each car." ^0 ``` ## Python (deterministic transpilation) ```python each_car_kmh = 50 car_kg = 1500 truck_kg = 15000 closing_speed_kmh = 2 * each_car_kmh momentum_eastbound = car_kg * each_car_kmh momentum_westbound = car_kg * each_car_kmh momentum_left_after_the_crash = momentum_eastbound - momentum_westbound speed_after_the_crash_kmh = int(momentum_left_after_the_crash / (2 * car_kg)) each_cars_change_of_speed_kmh = each_car_kmh - speed_after_the_crash_kmh each_cars_energy_vs_a_wall_at_100_per_mille = int(each_cars_change_of_speed_kmh * each_cars_change_of_speed_kmh * 1000 / (closing_speed_kmh * closing_speed_kmh)) car_change_of_speed_against_the_truck_kmh = int(2 * each_car_kmh * truck_kg / (car_kg + truck_kg)) truck_change_of_speed_kmh = int(2 * each_car_kmh * car_kg / (car_kg + truck_kg)) truck_outweighs_the_car_by = int(truck_kg / car_kg) print("each car : " + str(car_kg) + " kg at " + str(each_car_kmh) + " km/h") print("closing speed : " + str(closing_speed_kmh) + " km/h") print("momentum, one each way : " + str(momentum_eastbound) + " and " + str(momentum_westbound) + ", " + str(momentum_left_after_the_crash) + " left after the crash") print("speed after the crash : " + str(speed_after_the_crash_kmh) + " km/h") print("each car's change of speed : " + str(each_cars_change_of_speed_kmh) + " km/h, a wall at " + str(each_cars_change_of_speed_kmh)) print("each car's energy vs a wall at " + str(closing_speed_kmh) + " : " + str(each_cars_energy_vs_a_wall_at_100_per_mille) + " per mille") print("") print("a car against a truck : truck " + str(truck_kg) + " kg, " + str(truck_outweighs_the_car_by) + " times the car") print(" the car's change of speed : " + str(car_change_of_speed_against_the_truck_kmh) + " km/h") print(" the truck's change of speed : " + str(truck_change_of_speed_kmh) + " km/h") print("") print("the add-the-speeds reasoning") print(" each car : " + str(each_car_kmh) + " km/h") print(" closing speed : " + str(closing_speed_kmh) + " km/h") print(" outcome : both cars stop dead") print(" intent : how hard is this crash for each driver") print(" facts wrong : 0") print(" verdict : EACH DRIVER HITS A WALL AT " + str(closing_speed_kmh)) print("") print(" adding the two speeds is the part done right here, and it is") print(" why the cars really do close on each other at " + str(closing_speed_kmh) + " km/h") print("") print("the change of speed") print(" what the occupants feel : their own car's change of speed, over") print(" the time its front crumples") print(" two equal cars : equal and opposite momentum, " + str(momentum_left_after_the_crash) + " left, so both") print(" stop, and each changes speed by " + str(each_cars_change_of_speed_kmh) + " km/h") print(" a wall at " + str(closing_speed_kmh) + " : a change of " + str(closing_speed_kmh) + ", four times the energy; each") print(" car here takes " + str(each_cars_energy_vs_a_wall_at_100_per_mille) + " per mille of that") print(" when the closing speed bites : when the masses differ; the") print(" light car is flung backwards by the heavy one, a change of") print(" " + str(car_change_of_speed_against_the_truck_kmh) + " km/h against the truck's " + str(truck_change_of_speed_kmh)) print("") print("the lesson") print(" believed : a head-on at " + str(each_car_kmh) + " each is a wall at " + str(closing_speed_kmh)) print(" actual : for equal cars, a wall at " + str(each_cars_change_of_speed_kmh) + "; against a truck, nearly") print(" a wall at " + str(car_change_of_speed_against_the_truck_kmh)) print(" is the closing speed wrong : no; it is " + str(closing_speed_kmh)) print(" does the closing speed say what each car goes through : no;") print(" that depends on how the momentum is shared") print("") nc_change_of_speed_read_from_the_closing_speed_kmh = 100 nc_change_of_speed_read_from_the_momentum_kmh = 50 nc_kmh_the_momentum_reading_removes = 50 print("null control - read the crash from each car's change of speed") print(" change of speed, read from the closing speed : " + str(nc_change_of_speed_read_from_the_closing_speed_kmh) + " km/h") print(" change of speed, read from the momentum : " + str(nc_change_of_speed_read_from_the_momentum_kmh) + " km/h") print(" km/h the momentum reading removes : " + str(nc_kmh_the_momentum_reading_removes)) print(" no car and no speed changed; each car was judged by what") print(" happened to it, not by the gap the two of them closed") print("") print("what a closing speed of " + str(closing_speed_kmh) + " guarantees") print(" the cars approach each other at " + str(closing_speed_kmh) + " : exactly") print(" each car crashes as if into a wall at " + str(closing_speed_kmh) + " : not addressed; with") print(" equal masses each car's speed changes by " + str(each_cars_change_of_speed_kmh) + ", a wall at " + str(each_cars_change_of_speed_kmh) + " and") print(" " + str(each_cars_energy_vs_a_wall_at_100_per_mille) + " per mille of the energy - and it is the mass ratio that") print(" decides, a change of " + str(car_change_of_speed_against_the_truck_kmh) + " for the car against a truck") print("") print("a closing speed describes the gap, not the people in it; what each of them") print("goes through is their own change of speed, and that is shared out by mass") print("") print("The cars close at " + str(closing_speed_kmh) + " km/h - that is exact. But each car's occupants feel their") print("own change of speed, and two equal cars both stop: a change of " + str(each_cars_change_of_speed_kmh) + ", a wall at") print("" + str(each_cars_change_of_speed_kmh) + ", " + str(each_cars_energy_vs_a_wall_at_100_per_mille) + " per mille of the energy of one at " + str(closing_speed_kmh) + ", while the same car against a truck") print("changes by " + str(car_change_of_speed_against_the_truck_kmh) + ", until the crash is read by what happens to each car.") ``` ## stdout (executed) ```text each car : 1500 kg at 50 km/h closing speed : 100 km/h momentum, one each way : 75000 and 75000, 0 left after the crash speed after the crash : 0 km/h each car's change of speed : 50 km/h, a wall at 50 each car's energy vs a wall at 100 : 250 per mille a car against a truck : truck 15000 kg, 10 times the car the car's change of speed : 90 km/h the truck's change of speed : 9 km/h the add-the-speeds reasoning each car : 50 km/h closing speed : 100 km/h outcome : both cars stop dead intent : how hard is this crash for each driver facts wrong : 0 verdict : EACH DRIVER HITS A WALL AT 100 adding the two speeds is the part done right here, and it is why the cars really do close on each other at 100 km/h the change of speed what the occupants feel : their own car's change of speed, over the time its front crumples two equal cars : equal and opposite momentum, 0 left, so both stop, and each changes speed by 50 km/h a wall at 100 : a change of 100, four times the energy; each car here takes 250 per mille of that when the closing speed bites : when the masses differ; the light car is flung backwards by the heavy one, a change of 90 km/h against the truck's 9 the lesson believed : a head-on at 50 each is a wall at 100 actual : for equal cars, a wall at 50; against a truck, nearly a wall at 90 is the closing speed wrong : no; it is 100 does the closing speed say what each car goes through : no; that depends on how the momentum is shared null control - read the crash from each car's change of speed change of speed, read from the closing speed : 100 km/h change of speed, read from the momentum : 50 km/h km/h the momentum reading removes : 50 no car and no speed changed; each car was judged by what happened to it, not by the gap the two of them closed what a closing speed of 100 guarantees the cars approach each other at 100 : exactly each car crashes as if into a wall at 100 : not addressed; with equal masses each car's speed changes by 50, a wall at 50 and 250 per mille of the energy - and it is the mass ratio that decides, a change of 90 for the car against a truck a closing speed describes the gap, not the people in it; what each of them goes through is their own change of speed, and that is shared out by mass The cars close at 100 km/h - that is exact. But each car's occupants feel their own change of speed, and two equal cars both stop: a change of 50, a wall at 50, 250 per mille of the energy of one at 100, while the same car against a truck changes by 90, until the crash is read by what happens to each car. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done