William Tell
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:
William Tell must split the apple atop his son's head from a distance of sxO. When William aims directly at the apple the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speed of vzO?
Solution:
The question we have to answer is: At what angle is the maximum width m concerning meterpersecond? As in every ballistic-exercise the vertical motion determines the time of the motion. The arrow will travel for t t_uparrow + t_downarrow t_uparrow fracv_yg fracv_sinalphag Knowing that the width the arrow reaches at any angle alpha is: s_x v_x t v_cosalpha fracv_sinalphag fracv_^gsinalpha Here we used sinalphacosalpha frac sin alpha. We can solve this last for the angle alpha: alpha frac arcsinleft fracgs_xv_^ right ang.
William Tell must split the apple atop his son's head from a distance of sxO. When William aims directly at the apple the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speed of vzO?
Solution:
The question we have to answer is: At what angle is the maximum width m concerning meterpersecond? As in every ballistic-exercise the vertical motion determines the time of the motion. The arrow will travel for t t_uparrow + t_downarrow t_uparrow fracv_yg fracv_sinalphag Knowing that the width the arrow reaches at any angle alpha is: s_x v_x t v_cosalpha fracv_sinalphag fracv_^gsinalpha Here we used sinalphacosalpha frac sin alpha. We can solve this last for the angle alpha: alpha frac arcsinleft fracgs_xv_^ right ang.
Meta Information
Exercise:
William Tell must split the apple atop his son's head from a distance of sxO. When William aims directly at the apple the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speed of vzO?
Solution:
The question we have to answer is: At what angle is the maximum width m concerning meterpersecond? As in every ballistic-exercise the vertical motion determines the time of the motion. The arrow will travel for t t_uparrow + t_downarrow t_uparrow fracv_yg fracv_sinalphag Knowing that the width the arrow reaches at any angle alpha is: s_x v_x t v_cosalpha fracv_sinalphag fracv_^gsinalpha Here we used sinalphacosalpha frac sin alpha. We can solve this last for the angle alpha: alpha frac arcsinleft fracgs_xv_^ right ang.
William Tell must split the apple atop his son's head from a distance of sxO. When William aims directly at the apple the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speed of vzO?
Solution:
The question we have to answer is: At what angle is the maximum width m concerning meterpersecond? As in every ballistic-exercise the vertical motion determines the time of the motion. The arrow will travel for t t_uparrow + t_downarrow t_uparrow fracv_yg fracv_sinalphag Knowing that the width the arrow reaches at any angle alpha is: s_x v_x t v_cosalpha fracv_sinalphag fracv_^gsinalpha Here we used sinalphacosalpha frac sin alpha. We can solve this last for the angle alpha: alpha frac arcsinleft fracgs_xv_^ right ang.
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Schiefer Wurf auf Ebene [sx v0 alpha] by TeXercises
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Asked Quantity:
Winkel \(\theta\)
in
Radian \(\rm rad\)
Physical Quantity
Unit