Koordinatenpunkt treffen mittels Ballwurf
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
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Exercise:
Ein Ball wird mit vO gegen ein Ziel bei x_zxzO und y_zyzO geworfen. Der Abwurf erfolge wie üblich im Nullpunkt eines Koordinatensystems mit horizontaler x- und vertikaler y-Achse. abcliste abc Unter welchem Winkel alpha_ zur Horizontalen muss geworfen werden? abc Mit welcher minimalen Abwurfschnelligkeit v_ ist das Ziel noch erreichbar? abcliste
Solution:
% . Okt. Lie. * &texta Der Zielpunkt liegt auf der Wurfparabel: &y_zx_z tanalpha_ - fracg x_z^v_^cos^alpha_ &y_zx_z tanalpha_ - fracg x_z^v_^ + tan^alpha_ textquad quadratische Gleichung in tanalpha_ &tfrac tan^alpha_ - fracv_^gx_ztanalpha_ + tfrac + fracv_^ y_zg x_z^ &tanalpha_ fracv_^gx_z pm sqrt left fracv_^gx_z right^ - - fracv_^ y_zgx_z^ &alpha_ arctanleft fracv_^gx_z pm sqrt left fracv_^gx_z right^ - - fracv_^ y_zgx_z^ right &alpha_ arctanleft frac.sim/s^.sim/s^ .sim pm sqrt left frac.sim/s^.sim/s^ .sim right^ - - frac.sim/s^ .sim.sim/s^.sim^ right &alpha_ uulinesidegree text Bogenschuss quad uulinesidegree text Direktschuss &textb Der Radikand wird bei der Mindestgeschwindigkeit Null & left fracv_^gx_z right^ - fracv_^ y_zgx_z^ - textquad quadratische Gleichung in v_^ &v_^^ -gy_zv_^ - gx_z^ &v_^ gy_z pm tfracsqrt gy_z^ + gx_z^ &v_ sqrtgy_z pm tfracsqrt gy_z^ + gx_z^ sqrtgy_z pm g sqrt y_z^ + x_z^ &v_ sqrt .sim/s^ .sim pm .sim/s^ sqrt .sim^ + .sim^ &v_ uuline.sim/s textquad . Lösung hat negativen Radikanden * newpage
Ein Ball wird mit vO gegen ein Ziel bei x_zxzO und y_zyzO geworfen. Der Abwurf erfolge wie üblich im Nullpunkt eines Koordinatensystems mit horizontaler x- und vertikaler y-Achse. abcliste abc Unter welchem Winkel alpha_ zur Horizontalen muss geworfen werden? abc Mit welcher minimalen Abwurfschnelligkeit v_ ist das Ziel noch erreichbar? abcliste
Solution:
% . Okt. Lie. * &texta Der Zielpunkt liegt auf der Wurfparabel: &y_zx_z tanalpha_ - fracg x_z^v_^cos^alpha_ &y_zx_z tanalpha_ - fracg x_z^v_^ + tan^alpha_ textquad quadratische Gleichung in tanalpha_ &tfrac tan^alpha_ - fracv_^gx_ztanalpha_ + tfrac + fracv_^ y_zg x_z^ &tanalpha_ fracv_^gx_z pm sqrt left fracv_^gx_z right^ - - fracv_^ y_zgx_z^ &alpha_ arctanleft fracv_^gx_z pm sqrt left fracv_^gx_z right^ - - fracv_^ y_zgx_z^ right &alpha_ arctanleft frac.sim/s^.sim/s^ .sim pm sqrt left frac.sim/s^.sim/s^ .sim right^ - - frac.sim/s^ .sim.sim/s^.sim^ right &alpha_ uulinesidegree text Bogenschuss quad uulinesidegree text Direktschuss &textb Der Radikand wird bei der Mindestgeschwindigkeit Null & left fracv_^gx_z right^ - fracv_^ y_zgx_z^ - textquad quadratische Gleichung in v_^ &v_^^ -gy_zv_^ - gx_z^ &v_^ gy_z pm tfracsqrt gy_z^ + gx_z^ &v_ sqrtgy_z pm tfracsqrt gy_z^ + gx_z^ sqrtgy_z pm g sqrt y_z^ + x_z^ &v_ sqrt .sim/s^ .sim pm .sim/s^ sqrt .sim^ + .sim^ &v_ uuline.sim/s textquad . Lösung hat negativen Radikanden * newpage
Meta Information
Exercise:
Ein Ball wird mit vO gegen ein Ziel bei x_zxzO und y_zyzO geworfen. Der Abwurf erfolge wie üblich im Nullpunkt eines Koordinatensystems mit horizontaler x- und vertikaler y-Achse. abcliste abc Unter welchem Winkel alpha_ zur Horizontalen muss geworfen werden? abc Mit welcher minimalen Abwurfschnelligkeit v_ ist das Ziel noch erreichbar? abcliste
Solution:
% . Okt. Lie. * &texta Der Zielpunkt liegt auf der Wurfparabel: &y_zx_z tanalpha_ - fracg x_z^v_^cos^alpha_ &y_zx_z tanalpha_ - fracg x_z^v_^ + tan^alpha_ textquad quadratische Gleichung in tanalpha_ &tfrac tan^alpha_ - fracv_^gx_ztanalpha_ + tfrac + fracv_^ y_zg x_z^ &tanalpha_ fracv_^gx_z pm sqrt left fracv_^gx_z right^ - - fracv_^ y_zgx_z^ &alpha_ arctanleft fracv_^gx_z pm sqrt left fracv_^gx_z right^ - - fracv_^ y_zgx_z^ right &alpha_ arctanleft frac.sim/s^.sim/s^ .sim pm sqrt left frac.sim/s^.sim/s^ .sim right^ - - frac.sim/s^ .sim.sim/s^.sim^ right &alpha_ uulinesidegree text Bogenschuss quad uulinesidegree text Direktschuss &textb Der Radikand wird bei der Mindestgeschwindigkeit Null & left fracv_^gx_z right^ - fracv_^ y_zgx_z^ - textquad quadratische Gleichung in v_^ &v_^^ -gy_zv_^ - gx_z^ &v_^ gy_z pm tfracsqrt gy_z^ + gx_z^ &v_ sqrtgy_z pm tfracsqrt gy_z^ + gx_z^ sqrtgy_z pm g sqrt y_z^ + x_z^ &v_ sqrt .sim/s^ .sim pm .sim/s^ sqrt .sim^ + .sim^ &v_ uuline.sim/s textquad . Lösung hat negativen Radikanden * newpage
Ein Ball wird mit vO gegen ein Ziel bei x_zxzO und y_zyzO geworfen. Der Abwurf erfolge wie üblich im Nullpunkt eines Koordinatensystems mit horizontaler x- und vertikaler y-Achse. abcliste abc Unter welchem Winkel alpha_ zur Horizontalen muss geworfen werden? abc Mit welcher minimalen Abwurfschnelligkeit v_ ist das Ziel noch erreichbar? abcliste
Solution:
% . Okt. Lie. * &texta Der Zielpunkt liegt auf der Wurfparabel: &y_zx_z tanalpha_ - fracg x_z^v_^cos^alpha_ &y_zx_z tanalpha_ - fracg x_z^v_^ + tan^alpha_ textquad quadratische Gleichung in tanalpha_ &tfrac tan^alpha_ - fracv_^gx_ztanalpha_ + tfrac + fracv_^ y_zg x_z^ &tanalpha_ fracv_^gx_z pm sqrt left fracv_^gx_z right^ - - fracv_^ y_zgx_z^ &alpha_ arctanleft fracv_^gx_z pm sqrt left fracv_^gx_z right^ - - fracv_^ y_zgx_z^ right &alpha_ arctanleft frac.sim/s^.sim/s^ .sim pm sqrt left frac.sim/s^.sim/s^ .sim right^ - - frac.sim/s^ .sim.sim/s^.sim^ right &alpha_ uulinesidegree text Bogenschuss quad uulinesidegree text Direktschuss &textb Der Radikand wird bei der Mindestgeschwindigkeit Null & left fracv_^gx_z right^ - fracv_^ y_zgx_z^ - textquad quadratische Gleichung in v_^ &v_^^ -gy_zv_^ - gx_z^ &v_^ gy_z pm tfracsqrt gy_z^ + gx_z^ &v_ sqrtgy_z pm tfracsqrt gy_z^ + gx_z^ sqrtgy_z pm g sqrt y_z^ + x_z^ &v_ sqrt .sim/s^ .sim pm .sim/s^ sqrt .sim^ + .sim^ &v_ uuline.sim/s textquad . Lösung hat negativen Radikanden * newpage
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Koordinatenpunkt treffen mittels Ballwurf by TeXercises
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Fallgesetze: Schiefer Wurf by Lie