[br][i][color=#ff0000][b]Note[/b] [b](updated version of August 2017)[/b][br]A new version of this worksheet, named "Basketball 3D - v.3.4.4 (with rebounds)" has been posted at the page [url=https://www.geogebra.org/m/jM3YvFaw]https://www.geogebra.org/m/jM3YvFaw[/url].[br]It's a major update since it implements a different concept in the calculation of exact parabolic trajectories.[/color][/i][br]_____________________________________________________________________________________________[br][br]This Worksheet is a refinement of the previous material [url=https://www.geogebra.org/m/tMrZheXb]Basketball3D[/url] with the [b]addition of rebounds[/b] against the backboard and the rim together with the ball bounces when hitting the floor.[br][br]Addingr ebounds was not an easy task but greatly enhances the realism of the simulation and enrich the shooting practice with the possibility of [b]rimshots[/b] and [b]bankshots[/b]. [br] [br][b]Basic operation[/b]        [br]Click “[b][i]New Trial[/i][/b]” to position the shooter (the shooter will be placed randomly on the half-field). The position of the player can also be changed by manually moving the [b][i]A[/i][/b] point.[br]        [br]Through the sliders adjust the parameters "$\alpha$" (horizontal direction), "$\phi$" (vertical inclination) and "v[sub]0[/sub]“‍ to direct the shot to the basket.[br][br]Alternatively, in training mode, you can use the buttons to automatically set the parameters:[br][list][*]set $\alpha$: will set the right horizontal direction  [br][/*][*]set $\phi$: will set the right vertical slope of the shoot (given the actual value of v[sub]0[/sub])  [br][/*][*]set v[sub]0[/sub]: will set the right speed of the shot (given the actual value of $\phi$). [br][/*][/list]Click “[b][i]Shoot![/i][/b]” to start the animation.[br]See the result and repeat the operation[br][br]In game mode (“[i]New game[/i]” button) a countdown timer will be shown and different players can compare their score (in the set time) and performance.[br]In this mode it’s not possible to use the automatic settings for the direction and speed parameters and it’s not possible to repeat the same shot. [br][br][b]Other parameters and buttons[/b][br]“[i] $\alpha$[/i][i] fine tuning[/i]”: if checked the minimum and maximum values of the slider a will be closer to the correct horizontal direction, making easier to fine tuning its value.[br]“[i]surfdamp[/i]”: the amount of dumping or speed reduction of the ball after it hits a plane surface (the backboard or the floor). A value of 0.75 works fine.[br]“[i]ringdamp[/i]”: the amount of dumping or speed reduction of the ball after it hits the rim. A value of about 0.55 works fine.[br]“[i]spd[/i]”: the speed of the animation. Values in the range of 0.6-0.8 make the animation not too much slow and work fine. With greater values the accuracy of the rebounds decreases and there could even be no detection of the shot result.[br]“[i]SaveCstmIC[/i]” button: in case an interesting starting condition is found (i.e, one with nice rebounds) it’s[br]possible to save its relevant parameters (position of the player, direction and speed of the shot).[br]“[i]RestoreCstmIC[/i]” button: to restore the previously saved starting condition.[br][br][b]Visual aids[/b][br][list][*]The “h[sub]max[/sub]” (point) is the vertex of the initial parabola.[br][/*][*]A blue point on the backboard marks the point of impact of the ball with the backboard. In case of no impact this point is smaller and lighter and take the meaning of the point of intersection between the ball initial trajectory and the plane of the backboard.[br][/*][*]There is a moving gray disk representing the ball projection (shadow) on the floor.[br][/*][*]In the 3D window there are buttons to quickly change the point of view.[/*][br][/list][b]Possible issues[/b][br][list][*]In rare occasions I’ve noted that the rebound with the rim seems wrong.[br][/*][*]If the speed of the animation is too high rebounds and the result of the shot may not be[br]properly calculated.[/*][/list][b]Note[/b][br]Given complexity of the simulation it's advisable to download the .ggb file and run it through the Geogebra classic desktop program.[br]The web app may be rather slow and jerky.[br][br][br]