<p>DIY Worksheet: Free Fall with Constant Horizontal Speed LFS & DN</p><p>DIY Simulator - Free Fall with Constant Horizontal Speed – Make the Applet</p><p>2 1 Theorem: At time t, the height of an object dropped in free fall is: h(t )= ho - 16 t [ft]. Theorem: distance=speed*time</p><p>Open the interactivity (online or download): You should see something like this:</p><p>This is what we want to create. Now open GeoGebra to a new blank worksheet. 1. Create the 3 sliders: Time, h0 and vh.  Time is from 0 to 1 increment 0.1 (h0=10 gives droptime=0.89 so this covers all) Special: On the animation tab, change to increasing.  h0 is from 0 to 10 increment 0.1  vh is from 0 to 7 increment 0.1 Special: On the slider tab, change width to1402. 2. We want to calculate the droptime or the time it takes the object to drop to the ground. Think about what formula you need and define droptime in the input bar. 3. We want to calculate the dropdistance or the horizontal distance the object will travel before hitting the ground. Think about what formula you need and define dropdistance in the input bar.</p><p>1 2 For meters, we have: h(t )= ho - 4.9 t [m]. (Time t is in seconds.) 2 Always make your widths a multiple of the slider interval!</p><p> http://geogebrawiki.pbworks.com/DIY-Simulator-of-Free-Fall-Plus-Constant-Horizontal-Speed 1 DIY Worksheet: Free Fall with Constant Horizontal Speed LFS & DN</p><p>4. We want to define the green function h(x) for free fall – that is, for height as a function of time. We will use the variable x for time so that GeoGebra draws the function in the drawing pad. Also, we want to restrict it to reality. So we let x be from 0 to drop time. Before entering the function3: h(x)=Function[h0-16*x^2, 0, droptime] make sure you understand all of the parts of this definition! Remember this is not “how” the object drops but “when”. Now we want to make the animation. This is the part that integrates the Time slider with the physical dropping of the object. Remember we have 3 variables: time, horizontal distance and vertical height. We cannot graph 3 variables at the same time! </p><p>5. We make one point Ht = (Time, h(Time)). This will follow the function h(x) that we defined in 4. Create this point. Then right-click on the slider Time. Select animation on and check that this point follows the function h(x).</p><p>6. We make another point Hd that follows the physical dropping of the object. It will have a horizontal and vertical component. Both of these, that is, both the horizontal distance and the vertical height depend on time, but we will not see time on this point!</p><p>Define Hd=(vh* Time, h(Time)).  Understand that the x-coordinate is horizontal distance since it is horizontal speed multiplied by time. </p><p> Understand that the y-coordinates of both Ht and Hd are the same and why. 4 Right-click on Hd and select trace on. 7. Run the animator. You will see that the points continue “underground”. If you do not want this, right-click on both of the points, select “Object Properties” and on the advanced tab, type in the condition h(Time)>=0. Then click on Close.</p><p>3 If you are working with meters (and seconds): h0-4.9*x^2. That is, substitute 4.9 for 16. 4 In our simulator, because trace doesn’t work online, we put the “trace” in the background using a parametric curve.</p><p> http://geogebrawiki.pbworks.com/DIY-Simulator-of-Free-Fall-Plus-Constant-Horizontal-Speed 2 DIY Worksheet: Free Fall with Constant Horizontal Speed LFS & DN</p><p>Spreadsheet:  Click in A1 and type ="x=time" and hit enter.  Click in B1 and type ="y=height" and hit enter.  Click in C1 and type ="x=distance" and hit enter.</p><p>(Remember that for Ht, the x-coordinate is time and for Hd, the x-coordinate is distance.) Column A  Click in A2 and type 0 and hit enter.  Click in A3 and type =A2+0.1 and hit enter.  Click on A3, find the little box at bottom right and click and drag this down to A12.  To color this column red, click on A and then right-click on A1. Then, the menu will open with all the possibilities including “Object Properties”. Column B In B2 we want the height of the object at time A2. Can you think of a formula using h(x) and A2? Enter this formula. This formula should contain the cell reference A2!  Click in B2 and type = your formula and hit enter.  Click on B2, find the little box at bottom right and click and drag this down to B12. Column C In C2 we want the horizontal distance travelled by the object at time A2. Can you think of a formula using vh and A2? Enter this formula. This formula should contain the cell reference A2!  Click in C2 and type = your formula and hit enter.  Click on C2, find the little box at bottom right and click and drag this down to C12.</p><p>Testing, Testing, …  Change the values for Time, h0 and vh in both the online simulator and your simulator. Check that the values match.</p><p>You are done. Save your file. </p><p>P. S. If you want the pink curve, here is the definition: Curve[vh t, h0 - 16 t², t, 0, droptime]</p><p> http://geogebrawiki.pbworks.com/DIY-Simulator-of-Free-Fall-Plus-Constant-Horizontal-Speed 3</p>