1.3 Horizontal and vertical displacements: Once again, we use the fact that the horizontal motion of the projectile is a uniform motion (with a constant speed), and the vertical - uniformly accelerated motion. At any time t, the projectile's horizontal and vertical displacement are: x = Uot cos 00 , (5) y = vot sin 60 - 1 2gt2 1.4 Total time of motion Time of flight or total time of the whole journey is obtained from the y-component of Eq. (5) by setting y = 0 (the projectile hit the ground): 200 sin do . g (6) 1.5 Maximum height and range The greatest height that the object will reach is known as the peak of the object's motion. The increase in height will last until vy = 0, that is, H Uo sin 2 00 - 2g (7) The horizontal range L of the projectile is the horizontal distance it has traveled when it returns to its initial zero height (y = 0) L = Uo sin (200) . g (8) The range L has its maximum value when sin(200) = 1, which necessarily corresponds to 0 = 7/4 = 45.00. The range and the maximum height of the projectile does not depend upon its mass. 2 Useful resources 2.1 Educational websites . https://courses . lumenlearning . com/physics/chapter/3-4-projectile-motion . https://en. wikipedia. org/wiki/Projectile_motion . https://www. physicsclassroom. com/class/vectors/Lesson-2/What-is-a-Projectile 2.2 YouTube videos . https://www. youtube. com/watch?v=8NLzuURxFWY . https://www. youtube. com/watch?v=pZZt357pk-I . https://www. youtube. com/watch?v=aY8z2q044WA and many-many others available online.3 Procedure 1. Open our present online lab by clicking on the following link: https : [/phet . colorado . edu/en/simulation/proj tactilemot ion 3.1 Horizontal and vertical displacements of a projectile 2. Choose Lab window on the right side of your screen. 3. Set the initial speed of your projectile to be no : 15.0 m/s and the initial launch angle 90 : 45 0. Fire the projectile. 4. When you re the cannon, the path of the projectile is shown and with a marker drawn at every 0.1 sec of the projectile mot-ion time, as show in Fig. l mm 15m-s ii I z 4\" P'DIECNE' Mchnn Figure 1: (Color online) Schematics for Step 5. 5. Using both equations (5), calculate the horizontal and vertical position of the pro- jectile at the following time: 0.2 sec, 0.4 sec, 0.6sec., 0.8 sec, 1.0.sec., 1.2sec., 1.4 sec, 1.6 sec, 1.8 sec, 2.0 sec. Record your results in Table 1: |t.sec. 0.2| 0.4| 0.6| 0.8 1.0 1.2| 1.4| l.6| 1.8 2.0' Table 1. Theoretical. or calculated results for the horizontal 56(3) and vertical y(t) displacements of the projectile after each 0.2sec.. ~ In 6. Use the tracer tool to gather the data about the pro jectile's range and height at every other marked point of its trajectory which corresponds to 0.2 sec-increment. Record the obtained results into Table 2: 1, sec. 0.2 | 0.4 | 0.6 | 0.8 i 1.0 1.2 | 1.4 | 1.6 | 1.8 I 2.0 t 4 I (:1 m | | | 1 | | | | (r). | | | 1 | | | | Table 2. Experimental (measured) data for the horizontal :r(t) and vertical ya) displacements of the projectile after each 0.25m; 7. Are the theoretical and experimental results in Table 1 and Table 2 identical or just close to each other? 8. For the initial velocity and launch angle accepted and used in Step 9, calculate the maximum height of the projectile trajectory using Eq. (7) and its range from Eq. (8). v- -I 9. Verify your calculated results from the previous Step 14 using the tracer tool ".1; E at the highest and the terminal points of the investigated trajectory. A green dot at the top of the path shows the apex {or the highest point) of the path of our projectile. Lab Report am not going to demand any specic format or presentation style of your lab reports. This is completely 11p to you: vou can type it in MS Word. Latex. online Google documents. you can just scan the handwritten notes or even take the pictures on your phone. However, it is crucial that you: 1. D0 and properly explain all Steps which are printed in bold font in the Procedure section. Each such Step or a task (printed in Bold in you manual) should be properly addressed in your lab report in all detail. 2. Provide sample calculations which include all the equations, numbers and units for every calculation which you have performed for your lab experiment. Sample calculations means that you don't need to repeat. it in all detail if the same calculation is performed multiple times. such as lling a table for different values of a parameter. However. you will still need to do the calculation each time and put in the results into the table. 3. Conclusions, or main physics learning points from this experiment. Here. you should briey discuss which laws of physics you have learned and experimentally tested1 what kind(s) of phenomena you have dealt with. as well as your calculations and mathematical equations. Is this experiment helpful for your science education in general and why? Discuss the precision of your results and the percent errors. make any other comments you might think of (no one will be penalized for making critical comments regarding our course). This section should not exceed 1-5 lines. Here, I will specically value its originality, your own words and thoughts which are not copied from a textbook or someone else's report. Also, there are no specic requirements regarding the size of your lab report and, in fact' you cannot. nd a professor who wants to receive and grade 30mpage reports but all the questions need to be answered completely and in a lot of cases your score depends directly on the amount of relevant and original information which you provide within a specic response. The report should he submitted to Blackboard as an Assignment on or before the posted date or (as an exception. if the Blackboard submission system failed] sent by email to \" Dear Students' Please study the theoretical pre-lab materials, check the reconmmnded educational website and YouTube videos given below, and try to follow the step-by-step instruction. If you still have any questions regarding this lab, I will also he available by Skype. Zoom.com video conference or email during our regular class time and beyond in order to provide all the necessary assistance and guidance. Please contact me at_' with any questions, but please keep in mind that it might take me some considerable time to respond, especially if I receive too many of your messages at the same time. 1 Theory Projectile. motion is a form of motion experienced by an object or particle {a projectile) that is projected near the Earth's surface and moves along a curved path under the action of gravity only. Sometimes, the air resistance should be considered noticeable and included into the equations of motion. 1 .1 Acceleration a Since the only force acting on the moving projectile is the gravity force F}, = my}, where g = 9.81m/s-2 is the gravitational acceleration near the Earth surface, its horizontal acceleration equal to zero, and the vertical one - to g (downward direction): a, = U, {1) a\" = g. 1.2 Horizontal and vertical velocities The two component of the initial velocity exit = (1] and eyU. = U) could be found if the initial launch angle 6'\" is known: 1113,; = no cos 6'\" . {2) 'Uu'y = U\" Sill 6\" . The horizontal component of the velocity of the object remains unchanged throughout the motion. The vertical component of the velocity changes linearly. because of the two components of acceleration given in Eq. {1]. Using the velocity equation{s) for a uniform acceleration motion, we can write or = m1 = en cos 60 = const. {3) UH = en sin :90 gt . The magnitude of the velocity obtained under the Pythagorean theorem is \"roam = V \"E. + \"3MP = {\"0 (308 9M2 + (\"0 511190 i .002 - {4) It obviously depends on time