Raketengleichung
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
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Exercise:
Eine Rakete verliert kontinuierlich Treibstoff. Die Ausströmgeschwindigkeit des Treibstoffs beträgt u konstant relativ zur Rakete. Die Masse der Rakete zum Zeitpunkt t ist gegeben durch mt m_ - r t mit Anfangsmasse m_ Abbaurate r und leq t fracm_r maximaler Brenndauer. Bestimme die Geschwindigkeit vt der Rakete in Abhängigkeit von der Zeit.
Solution:
Schub der Rakete: * ma u fracmboxdmmboxdt F_textscriptsize thrust * Raketengleichung: * mfracmboxdvmboxdt ufracmboxdmmboxdt + F_textscriptsize ext * Start von der Erde d.h. F_textscriptsize ext-mg: * fracmboxdvmboxdt fracumfracmboxdmmboxdt -g v_v_a uln leftfracm_am_eright-gt_v *
Eine Rakete verliert kontinuierlich Treibstoff. Die Ausströmgeschwindigkeit des Treibstoffs beträgt u konstant relativ zur Rakete. Die Masse der Rakete zum Zeitpunkt t ist gegeben durch mt m_ - r t mit Anfangsmasse m_ Abbaurate r und leq t fracm_r maximaler Brenndauer. Bestimme die Geschwindigkeit vt der Rakete in Abhängigkeit von der Zeit.
Solution:
Schub der Rakete: * ma u fracmboxdmmboxdt F_textscriptsize thrust * Raketengleichung: * mfracmboxdvmboxdt ufracmboxdmmboxdt + F_textscriptsize ext * Start von der Erde d.h. F_textscriptsize ext-mg: * fracmboxdvmboxdt fracumfracmboxdmmboxdt -g v_v_a uln leftfracm_am_eright-gt_v *
Meta Information
Exercise:
Eine Rakete verliert kontinuierlich Treibstoff. Die Ausströmgeschwindigkeit des Treibstoffs beträgt u konstant relativ zur Rakete. Die Masse der Rakete zum Zeitpunkt t ist gegeben durch mt m_ - r t mit Anfangsmasse m_ Abbaurate r und leq t fracm_r maximaler Brenndauer. Bestimme die Geschwindigkeit vt der Rakete in Abhängigkeit von der Zeit.
Solution:
Schub der Rakete: * ma u fracmboxdmmboxdt F_textscriptsize thrust * Raketengleichung: * mfracmboxdvmboxdt ufracmboxdmmboxdt + F_textscriptsize ext * Start von der Erde d.h. F_textscriptsize ext-mg: * fracmboxdvmboxdt fracumfracmboxdmmboxdt -g v_v_a uln leftfracm_am_eright-gt_v *
Eine Rakete verliert kontinuierlich Treibstoff. Die Ausströmgeschwindigkeit des Treibstoffs beträgt u konstant relativ zur Rakete. Die Masse der Rakete zum Zeitpunkt t ist gegeben durch mt m_ - r t mit Anfangsmasse m_ Abbaurate r und leq t fracm_r maximaler Brenndauer. Bestimme die Geschwindigkeit vt der Rakete in Abhängigkeit von der Zeit.
Solution:
Schub der Rakete: * ma u fracmboxdmmboxdt F_textscriptsize thrust * Raketengleichung: * mfracmboxdvmboxdt ufracmboxdmmboxdt + F_textscriptsize ext * Start von der Erde d.h. F_textscriptsize ext-mg: * fracmboxdvmboxdt fracumfracmboxdmmboxdt -g v_v_a uln leftfracm_am_eright-gt_v *
Contained in these collections:
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Newtonsche Gesetze 2 by uz