Initial speed for Basketball throw
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
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
Zeit \(t\) / Kraft \(F\) / Geschwindigkeit \(v\) / Strecke \(s\) / Beschleunigung \(a\) / Winkel \(\theta\) /
The following formulas must be used to solve the exercise:
\(s = \dfrac{1}{2}at^2+v_0 t \quad \) \(s = vt \quad \) \(F_x = F \cos\alpha \quad F_y = F \sin\alpha \quad \)
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Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
A basketball leaves a player's hands at a height of haO above the floor. The basket is hbO above the floor. The player likes to shoot the ball at a alO angle. If the shot is made from a horizontal distance of sxO and must be accurat to pmtolO horizontally what is the range of initial speeds allowed to make the basket?
Solution:
The minimal and maximal allowed horizontal distances are s_xmin saF sx - tol sa s_xmax sbF sx + tol sb The ball is glqq goodgrqq if it is thrown within this distance range sa dots sb. Two s determine each motion of a thrown object: h fracgt^+v_y t fracgt^ + v_ sinalpha t s_x v_x t v_ cosalpha t Since we do neither know the duration t of the throw nor the initial velocity v_ we can't work with only one of them. Eliminating the time t which is not explicitly of erest by subsituting it in one with the expression obtained from the other we up with: h fracgt^ + v_ sinalpha t fracgleftfracs_xv_xright^ + v_ sinalpha leftfracs_xv_xright fracgleftfracs_xv_ cosalpharight^ + v_ sinalpha leftfracs_xv_ cosalpharight fracg fracs_x^v_^cos^alpha + s_xtanalpha Solved for the initial speed v_ we get: v_ sqrtfracgs_x^cos^alphafracs_x tanalpha - h where h is the height difference between the basket and the release po Delta h hF hb - ha h For the minimal and maximal distance this gives Geg h_a ha h_b hb alpha al s_x sx Delta s_x tol GesMinimum initial speedv_minsimeterpersecond GesMaximum initial speedv_maxsimeterpersecond v_min sqrtfracg s_xmin^ cosleftalpharight^ lefts_xmin tanleftalpharight - Delta hright sqrtfracg leftsaFright^ cosleftalpharight^ leftleftsaFright tanleftalpharight - hFright sqrtfracncg leftsx - tolright^ cosleftalright^ leftleftsx - tolright tanleftalright - lefthb - harightright va approx vaP v_max sqrtfracg s_xmax^ cosleftalpharight^ lefts_xmax tanleftalpharight - Delta hright sqrtfracg leftsbFright^ cosleftalpharight^ leftleftsbFright tanleftalpharight - hFright sqrtfracncg leftsx + tolright^ cosleftalright^ leftleftsx + tolright tanleftalright - lefthb - harightright vb approx vbP v_min vaF vaP v_max vbF vbP The basketball player has to shoot the ball within a speed range of va dots vb.
A basketball leaves a player's hands at a height of haO above the floor. The basket is hbO above the floor. The player likes to shoot the ball at a alO angle. If the shot is made from a horizontal distance of sxO and must be accurat to pmtolO horizontally what is the range of initial speeds allowed to make the basket?
Solution:
The minimal and maximal allowed horizontal distances are s_xmin saF sx - tol sa s_xmax sbF sx + tol sb The ball is glqq goodgrqq if it is thrown within this distance range sa dots sb. Two s determine each motion of a thrown object: h fracgt^+v_y t fracgt^ + v_ sinalpha t s_x v_x t v_ cosalpha t Since we do neither know the duration t of the throw nor the initial velocity v_ we can't work with only one of them. Eliminating the time t which is not explicitly of erest by subsituting it in one with the expression obtained from the other we up with: h fracgt^ + v_ sinalpha t fracgleftfracs_xv_xright^ + v_ sinalpha leftfracs_xv_xright fracgleftfracs_xv_ cosalpharight^ + v_ sinalpha leftfracs_xv_ cosalpharight fracg fracs_x^v_^cos^alpha + s_xtanalpha Solved for the initial speed v_ we get: v_ sqrtfracgs_x^cos^alphafracs_x tanalpha - h where h is the height difference between the basket and the release po Delta h hF hb - ha h For the minimal and maximal distance this gives Geg h_a ha h_b hb alpha al s_x sx Delta s_x tol GesMinimum initial speedv_minsimeterpersecond GesMaximum initial speedv_maxsimeterpersecond v_min sqrtfracg s_xmin^ cosleftalpharight^ lefts_xmin tanleftalpharight - Delta hright sqrtfracg leftsaFright^ cosleftalpharight^ leftleftsaFright tanleftalpharight - hFright sqrtfracncg leftsx - tolright^ cosleftalright^ leftleftsx - tolright tanleftalright - lefthb - harightright va approx vaP v_max sqrtfracg s_xmax^ cosleftalpharight^ lefts_xmax tanleftalpharight - Delta hright sqrtfracg leftsbFright^ cosleftalpharight^ leftleftsbFright tanleftalpharight - hFright sqrtfracncg leftsx + tolright^ cosleftalright^ leftleftsx + tolright tanleftalright - lefthb - harightright vb approx vbP v_min vaF vaP v_max vbF vbP The basketball player has to shoot the ball within a speed range of va dots vb.
Meta Information
Exercise:
A basketball leaves a player's hands at a height of haO above the floor. The basket is hbO above the floor. The player likes to shoot the ball at a alO angle. If the shot is made from a horizontal distance of sxO and must be accurat to pmtolO horizontally what is the range of initial speeds allowed to make the basket?
Solution:
The minimal and maximal allowed horizontal distances are s_xmin saF sx - tol sa s_xmax sbF sx + tol sb The ball is glqq goodgrqq if it is thrown within this distance range sa dots sb. Two s determine each motion of a thrown object: h fracgt^+v_y t fracgt^ + v_ sinalpha t s_x v_x t v_ cosalpha t Since we do neither know the duration t of the throw nor the initial velocity v_ we can't work with only one of them. Eliminating the time t which is not explicitly of erest by subsituting it in one with the expression obtained from the other we up with: h fracgt^ + v_ sinalpha t fracgleftfracs_xv_xright^ + v_ sinalpha leftfracs_xv_xright fracgleftfracs_xv_ cosalpharight^ + v_ sinalpha leftfracs_xv_ cosalpharight fracg fracs_x^v_^cos^alpha + s_xtanalpha Solved for the initial speed v_ we get: v_ sqrtfracgs_x^cos^alphafracs_x tanalpha - h where h is the height difference between the basket and the release po Delta h hF hb - ha h For the minimal and maximal distance this gives Geg h_a ha h_b hb alpha al s_x sx Delta s_x tol GesMinimum initial speedv_minsimeterpersecond GesMaximum initial speedv_maxsimeterpersecond v_min sqrtfracg s_xmin^ cosleftalpharight^ lefts_xmin tanleftalpharight - Delta hright sqrtfracg leftsaFright^ cosleftalpharight^ leftleftsaFright tanleftalpharight - hFright sqrtfracncg leftsx - tolright^ cosleftalright^ leftleftsx - tolright tanleftalright - lefthb - harightright va approx vaP v_max sqrtfracg s_xmax^ cosleftalpharight^ lefts_xmax tanleftalpharight - Delta hright sqrtfracg leftsbFright^ cosleftalpharight^ leftleftsbFright tanleftalpharight - hFright sqrtfracncg leftsx + tolright^ cosleftalright^ leftleftsx + tolright tanleftalright - lefthb - harightright vb approx vbP v_min vaF vaP v_max vbF vbP The basketball player has to shoot the ball within a speed range of va dots vb.
A basketball leaves a player's hands at a height of haO above the floor. The basket is hbO above the floor. The player likes to shoot the ball at a alO angle. If the shot is made from a horizontal distance of sxO and must be accurat to pmtolO horizontally what is the range of initial speeds allowed to make the basket?
Solution:
The minimal and maximal allowed horizontal distances are s_xmin saF sx - tol sa s_xmax sbF sx + tol sb The ball is glqq goodgrqq if it is thrown within this distance range sa dots sb. Two s determine each motion of a thrown object: h fracgt^+v_y t fracgt^ + v_ sinalpha t s_x v_x t v_ cosalpha t Since we do neither know the duration t of the throw nor the initial velocity v_ we can't work with only one of them. Eliminating the time t which is not explicitly of erest by subsituting it in one with the expression obtained from the other we up with: h fracgt^ + v_ sinalpha t fracgleftfracs_xv_xright^ + v_ sinalpha leftfracs_xv_xright fracgleftfracs_xv_ cosalpharight^ + v_ sinalpha leftfracs_xv_ cosalpharight fracg fracs_x^v_^cos^alpha + s_xtanalpha Solved for the initial speed v_ we get: v_ sqrtfracgs_x^cos^alphafracs_x tanalpha - h where h is the height difference between the basket and the release po Delta h hF hb - ha h For the minimal and maximal distance this gives Geg h_a ha h_b hb alpha al s_x sx Delta s_x tol GesMinimum initial speedv_minsimeterpersecond GesMaximum initial speedv_maxsimeterpersecond v_min sqrtfracg s_xmin^ cosleftalpharight^ lefts_xmin tanleftalpharight - Delta hright sqrtfracg leftsaFright^ cosleftalpharight^ leftleftsaFright tanleftalpharight - hFright sqrtfracncg leftsx - tolright^ cosleftalright^ leftleftsx - tolright tanleftalright - lefthb - harightright va approx vaP v_max sqrtfracg s_xmax^ cosleftalpharight^ lefts_xmax tanleftalpharight - Delta hright sqrtfracg leftsbFright^ cosleftalpharight^ leftleftsbFright tanleftalpharight - hFright sqrtfracncg leftsx + tolright^ cosleftalright^ leftleftsx + tolright tanleftalright - lefthb - harightright vb approx vbP v_min vaF vaP v_max vbF vbP The basketball player has to shoot the ball within a speed range of va dots vb.
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