demoscode

i. Initial velocity v 0 = 15 m / s ii. Initial angle θ 0 = 30 ° iii. g = 9.81 m / s 2 c. Desmos recognizes Greek letters. If you type “theta” in the expression, Desmos will convert it to θ . This also works for pi, which converts to π . d. Desmos does not use units , so just enter the numbers without units. Use a note to list units in your simulation if you are having trouble remembering them. e. Click on the wrench in the upper right corner of the graph and click “Degrees” at the bottom of the pop-up window. This sets the calculator to degrees instead of radians. Write notes in your expression list for the rest of these steps to illustrate the purpose of these expressions to the reader. 3. Write expressions that calculate the x and y components of the initial velocity, v 0 x and v 0 y , from your input variables. Their numerical values should appear in the expression line. Verify that they are correct before continuing. 4. Write expressions for the x and y coordinates of the particle as the relate to time, t . Use x P and y P to represent the position. These equations can be determined from the equations for projectile motion found in the text. 5. Create a labeled point that represents the particle. a. Type ( x P , y P ) to create a point. b. Label the point “particle” when the prompt appears in the expression line. (See Desmos Resources above for video.) 6. Scroll up to the t slider in the expression list and click the play button in that line to set ▶ the simulation in motion. a. Verify that the motion of the particle resembles projectile motion. b. If the particle is moving too fast to see, click the arrows below the play button and set the Speed to a lower value. c. If you would like to make the particle move more smoothly, set the Step to a lower value, like 0.1. d. Change the input variables and note how this changes the projectile’s path. e. There are arrows below the play button that represent different play modes. Set the simulation to run once and then stop. 7. Note that the projectile might not stop when it hits the x axis. We could calculate the projectile’s time in the air manually and set that value as the maximum value for t , but instead we will have Desmos calculate this for us using the input variables. This has the added bonus of avoiding recalculating if the input variables are changed. a. Using the input variables, calculate the time that the particle will hit the ground, that is, hit the x axis. Use the variable t f for this variable. b. Scroll up to the t slider and insert t f as the maximum value. Note that Desmos does not care if variables calculated lower down on the expression list are used earlier in the list. In other words, Desmos does not follow the expression list in order.

Now we will use what you have learned in the previous section to simulate the path of the water in this problem. The water droplet will move like a projectile. Before we work on the simulation, let’s prepare some equations. Write an equation that represents the line of the ramp. Note that the ramp starts at the origin. Use the equation editor in Google Docs to write your equation. y=3/4x Using kinematics equations, write an equation that relates the x coordinate of the position of the water droplet to time. Write an equation that relates the y coordinate of the position of the water droplet to time. x=(-v_osin36.9)t, y=(v_ocos36.9)t+.5(-9.81)t^2 Using the equations you wrote above, calculate the time that it will take for the water droplet to hit the ramp. Show your work below by either using the equation editor or writing your work on a sheet of paper, taking a picture with your phone, and uploading it to this document.

Question 3: What other suggestions do you have for improving this assignment? What other activities could be added to enhance student learning? I think figuring out the equations on paper makes it easier for me to figure out the equations.