Fallgesetze: Horizontaler Wurf 1
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 Schneeball wird mit .sim/s in horizontaler Richtung von der Aussichtsterrasse eines Bergrestaurants geworfen. Die Abwurfstelle sei der Nullpunkt des Koordinatensystems mit der x-Achse in horizontaler und der y-Achse in vertikaler Richtung aufwärts positiv. a Bei welcher Koordinate ist der Ball nach .sis? Berechnen Sie auch die Geschwindigkeit x- und y-Komponente Betrag Winkel zur Horizontalen zu diesem Zeitpunkt. b Der Ball habe sich in horizontaler Richtung .sim bewegt. Zu welchem Zeitpunkt ist er da? Wie lautet die zugehörige y-Koordinate? c Der Ball sei .sim gefallen. Wie lange hat das gedauert? Wie lautet die zugehörige x-Koordinate? Berechnen Sie auch den Betrag der Geschwindigkeit.
Solution:
a * x v_x t .sim/s .sis uulinesim y - frac g t^ - frac .sim s^- .sis^ uulinsim v_x v_x .sim/s v_y v_y-g t -.sim s^- .sis uulinsim/s v sqrtv_x^ + v_y^ sqrt leftv_x right^ + left-g t right^ sqrt left.sim/s right^ + left.sim s^- .sis right^ uuline.sim/s alpha arctan fracv_xv_y arctan fracv_x-gt arctan frac.sim/s-.sim s^- .sis uulin^circ * b * t fracxv_x frac.sim.sim/s uuline.sis y -frac g t^ -frac g left fracxv_x right^ -frac .sim s^- left frac.sim.sim/s right^ uulin.sim * c * y -frac gt^ Rightarrow t sqrtfrac-yg sqrtfrac- -.sim.sim s^- .sis uuline.sis x v_x t v_x sqrtfrac-yg .sim/s sqrtfrac- -.sim.sim s^- uulinesim v_y^ v_y^ -gy -gy Rightarrow v sqrtleftv_x right^ + leftv_y right^ sqrtleftv_x right^ -gy sqrtleft.sim/s right^ - -.sim.sim s^- uulinesim/s * newpage
Ein Schneeball wird mit .sim/s in horizontaler Richtung von der Aussichtsterrasse eines Bergrestaurants geworfen. Die Abwurfstelle sei der Nullpunkt des Koordinatensystems mit der x-Achse in horizontaler und der y-Achse in vertikaler Richtung aufwärts positiv. a Bei welcher Koordinate ist der Ball nach .sis? Berechnen Sie auch die Geschwindigkeit x- und y-Komponente Betrag Winkel zur Horizontalen zu diesem Zeitpunkt. b Der Ball habe sich in horizontaler Richtung .sim bewegt. Zu welchem Zeitpunkt ist er da? Wie lautet die zugehörige y-Koordinate? c Der Ball sei .sim gefallen. Wie lange hat das gedauert? Wie lautet die zugehörige x-Koordinate? Berechnen Sie auch den Betrag der Geschwindigkeit.
Solution:
a * x v_x t .sim/s .sis uulinesim y - frac g t^ - frac .sim s^- .sis^ uulinsim v_x v_x .sim/s v_y v_y-g t -.sim s^- .sis uulinsim/s v sqrtv_x^ + v_y^ sqrt leftv_x right^ + left-g t right^ sqrt left.sim/s right^ + left.sim s^- .sis right^ uuline.sim/s alpha arctan fracv_xv_y arctan fracv_x-gt arctan frac.sim/s-.sim s^- .sis uulin^circ * b * t fracxv_x frac.sim.sim/s uuline.sis y -frac g t^ -frac g left fracxv_x right^ -frac .sim s^- left frac.sim.sim/s right^ uulin.sim * c * y -frac gt^ Rightarrow t sqrtfrac-yg sqrtfrac- -.sim.sim s^- .sis uuline.sis x v_x t v_x sqrtfrac-yg .sim/s sqrtfrac- -.sim.sim s^- uulinesim v_y^ v_y^ -gy -gy Rightarrow v sqrtleftv_x right^ + leftv_y right^ sqrtleftv_x right^ -gy sqrtleft.sim/s right^ - -.sim.sim s^- uulinesim/s * newpage
Meta Information
Exercise:
Ein Schneeball wird mit .sim/s in horizontaler Richtung von der Aussichtsterrasse eines Bergrestaurants geworfen. Die Abwurfstelle sei der Nullpunkt des Koordinatensystems mit der x-Achse in horizontaler und der y-Achse in vertikaler Richtung aufwärts positiv. a Bei welcher Koordinate ist der Ball nach .sis? Berechnen Sie auch die Geschwindigkeit x- und y-Komponente Betrag Winkel zur Horizontalen zu diesem Zeitpunkt. b Der Ball habe sich in horizontaler Richtung .sim bewegt. Zu welchem Zeitpunkt ist er da? Wie lautet die zugehörige y-Koordinate? c Der Ball sei .sim gefallen. Wie lange hat das gedauert? Wie lautet die zugehörige x-Koordinate? Berechnen Sie auch den Betrag der Geschwindigkeit.
Solution:
a * x v_x t .sim/s .sis uulinesim y - frac g t^ - frac .sim s^- .sis^ uulinsim v_x v_x .sim/s v_y v_y-g t -.sim s^- .sis uulinsim/s v sqrtv_x^ + v_y^ sqrt leftv_x right^ + left-g t right^ sqrt left.sim/s right^ + left.sim s^- .sis right^ uuline.sim/s alpha arctan fracv_xv_y arctan fracv_x-gt arctan frac.sim/s-.sim s^- .sis uulin^circ * b * t fracxv_x frac.sim.sim/s uuline.sis y -frac g t^ -frac g left fracxv_x right^ -frac .sim s^- left frac.sim.sim/s right^ uulin.sim * c * y -frac gt^ Rightarrow t sqrtfrac-yg sqrtfrac- -.sim.sim s^- .sis uuline.sis x v_x t v_x sqrtfrac-yg .sim/s sqrtfrac- -.sim.sim s^- uulinesim v_y^ v_y^ -gy -gy Rightarrow v sqrtleftv_x right^ + leftv_y right^ sqrtleftv_x right^ -gy sqrtleft.sim/s right^ - -.sim.sim s^- uulinesim/s * newpage
Ein Schneeball wird mit .sim/s in horizontaler Richtung von der Aussichtsterrasse eines Bergrestaurants geworfen. Die Abwurfstelle sei der Nullpunkt des Koordinatensystems mit der x-Achse in horizontaler und der y-Achse in vertikaler Richtung aufwärts positiv. a Bei welcher Koordinate ist der Ball nach .sis? Berechnen Sie auch die Geschwindigkeit x- und y-Komponente Betrag Winkel zur Horizontalen zu diesem Zeitpunkt. b Der Ball habe sich in horizontaler Richtung .sim bewegt. Zu welchem Zeitpunkt ist er da? Wie lautet die zugehörige y-Koordinate? c Der Ball sei .sim gefallen. Wie lange hat das gedauert? Wie lautet die zugehörige x-Koordinate? Berechnen Sie auch den Betrag der Geschwindigkeit.
Solution:
a * x v_x t .sim/s .sis uulinesim y - frac g t^ - frac .sim s^- .sis^ uulinsim v_x v_x .sim/s v_y v_y-g t -.sim s^- .sis uulinsim/s v sqrtv_x^ + v_y^ sqrt leftv_x right^ + left-g t right^ sqrt left.sim/s right^ + left.sim s^- .sis right^ uuline.sim/s alpha arctan fracv_xv_y arctan fracv_x-gt arctan frac.sim/s-.sim s^- .sis uulin^circ * b * t fracxv_x frac.sim.sim/s uuline.sis y -frac g t^ -frac g left fracxv_x right^ -frac .sim s^- left frac.sim.sim/s right^ uulin.sim * c * y -frac gt^ Rightarrow t sqrtfrac-yg sqrtfrac- -.sim.sim s^- .sis uuline.sis x v_x t v_x sqrtfrac-yg .sim/s sqrtfrac- -.sim.sim s^- uulinesim v_y^ v_y^ -gy -gy Rightarrow v sqrtleftv_x right^ + leftv_y right^ sqrtleftv_x right^ -gy sqrtleft.sim/s right^ - -.sim.sim s^- uulinesim/s * newpage
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