INCREASING EDUCATIONAL EFFICIENCY THROUGH MODELING THE MOTION OF AN OBJECT THROWED AT AN ANGLE TO THE HORIZON

SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 154 INCREASING EDUCATIONAL EFFICIENCY THROUGH MODELING THE MOTION OF AN OBJECT THROWED AT AN ANGLE TO THE HORIZON S.D. Jonibekova Andijan State University, doctoral student https://doi.org/10.5281/zenodo.17844450 Abstract. The article considers the modeling of physical processes using the graphical capabilities of the Visual Basic programming language on the example of the motion of an object thrown at an angle to the horizon. A program has been created in Visual Basic to model the considered process. A distinctive feature of the program is that the user can quickly independently execute it, observe, compare and draw conclusions. This program can be used in independent learning and physics teaching processes. Keywords: throwing angle, initial speed, coordinates, resistance force, height, range, flight time, target, modeling, Visual Basic. Introduction As we know, the 21st century has brought new trends to education. New technologies are being created, new teaching methods are being developed, innovative lesson plans are emerging, curricula and textbooks are being updated, and so on. Today, developing students' creative abilities is especially important, as cultivating creative individuals through every subject has become a top priority. People today need many things: Pushkin's poetry, Beethoven's music, Einstein's theory of relativity, astronautics, bionics, microelectronics, and the rigor of mathematical and physical formulas. To prevent learning from becoming boring and monotonous, it is necessary to choose technologies based on instilling in students a pleasant sense of novelty in each lesson and activating learning activities through various modern pedagogical technologies in the areas of modernization [1, 2]. The introduction of new educational technologies into the educational process is changing teaching methods, enabling the use of physical process modeling, animation, and personal computers alongside traditional methods, techniques, and methodologies. These technologies help create basic visual images, integrate interdisciplinary knowledge, develop creative thinking, and enhance student learning [3, 4]. Currently, it is impossible to imagine processing information transmitted from spacecraft, controlling particle motion in accelerators, conducting high-precision experiments, and solving complex problems in theoretical physics without computers. On the other hand, the problems of general physics are very simple, and the numbers involved are generalized. This is crucial for a basic understanding and study of physical laws. However, virtually all physical problems encountered in real life cannot be solved analytically and require the use of computers. Therefore, every physicist must be able to independently solve problems on a computer, and conducting scientific research in this area is one of the most pressing challenges of our time [5, 6]. When mastering physics, the following issues related to teaching methods are relevant. They are determined by the content of physics and its characteristics, the ability of physics teaching materials to adequately reflect physical processes in nature, the demonstration of the essence of all SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 155 physical processes through experiments and laboratory work and the generalization of experimental results, the complexity of calculations when solving physics problems, and the correct reflection in the minds of students of ideas about physical processes in the microand macroworld: • the difficulty of implementing live, dynamic, moving, and animated demonstrations based on modeling when teaching topics devoted to invisible physical microand macroprocesses, in particular processes occurring at extremely high or very low speeds, based on traditional "paper" teaching technologies; • reliance on oral presentation when teaching topics including experiments that cannot be demonstrated in a laboratory setting, which leads to the impossibility of adequately developing students' imaginations; • the impossibility of using technically and technologically complex equipment requiring high precision to demonstrate certain physical processes, and, as a result, the impossibility of developing the relevant knowledge and imagination in students; • the lack of development of a methodology for conducting frontal exhibition and demonstration experiments, the demonstration of which is provided for by the physics curriculum in the lesson, and the organizational and pedagogical foundations for their implementation, as well as the limited possibilities for conducting them; • the need for complex mathematical calculations that do not correspond to the level of students' mathematical knowledge when explaining certain topics and solving problems in physics, etc. [7, 8] Therefore, attention should be paid to the technologies, methods, and teaching aids used, and the opportunities available to overcome these challenges and thereby achieve effective learning. The use of ICT is necessary and desirable for solving the above-mentioned problems in physics teaching [9, 10]. This article examines the application of new information technologies to solving physics problems related to the motion of a body thrown at an angle to the horizontal. 2. Materials and Methods As is well known, solving many physics problems boils down to solving transcendental and differential equations, plotting function graphs, calculating definite integrals, and so on, all using numerical methods. To simplify the solution of such problems on a computer, the author has created a program. The program has the *.exe extension and is of great scientific and practical value due to its ability to be used on any computer, its small size, and the lack of a need to write a program. To demonstrate the capabilities of this program, we will consider the motion of a body thrown at an angle to the horizontal. The program is designed to study the motion of a body thrown at an angle to the horizontal using a computer, both without and with air resistance. It allows for animated observation of the body's motion, determining the launch angle for a known initial velocity and target coordinates, and observing its impact with the target. As is known [7], the coordinates of a body thrown at an angle to the horizon without taking into account air resistance depend on time as ,cos 0tvx   (1) 2 sin 2 0 gt tvy   (2) And the trajectory of motion obeys a parabolic law SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 156   22 0 2 cos2v gx xtgy  (3) Flight time, flight range, and ascent altitude are determined by the expressions g v t  sin2 0  (4) g v l  2sin2 2 0  (5) g v h2 sin22 0   (6) Taking into account air resistance, the main characteristics and trajectory of movement are determined by solving the differential equation )('' kvmgmr  (7) where k is a constant. 3. Results and Discussion Let's consider the following problems. Problem 1. How long will it take for a body thrown at an angle of 30° to the horizontal with an initial velocity of 5 m/s to travel a height of 20 cm? Solution: It is known that the ordinate of a body thrown at an angle to the horizontal is related to time by the equation: 2 sin 2 0 gt tvy   (8) In this equation, replace y with h and write it as: 0 2 sin 2 0 gt tvh  (9) Substitute the numerical values of the quantities and denote "t" by "x." Selecting the "Solving Transcendental Equations" section of the program, entering "0.2-2.5*x+5*x^2" in the "The form of the equation" window, and clicking "Ok" yields the result x=0.053 (Fig. 1) Fig. 1. Solution of transcendental equations. SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 157 Problem 2. Find the acceleration of gravity if a body thrown at an angle of 30° to the horizontal travels a height of 0.2 m in 0.1 s and 0.3 m in 0.2 s. Solution. It is known that the height of a body thrown at an angle to the horizontal at time t is determined by the formula 2 sin 2 0gt tvh   (11) If we substitute the heights at t1 = 0.1 s and t2 = 0.2 s into this formula, we obtain a system of equations      32.0 205.05.0 0 0 gv gv (12) If we select the "Solving a System of Linear Equations" section of the program and enter "2" in cell "N", "0.5" in cell "A11", "-0.05" in cell "A12", "1" in cell "A21", "-0.2" in cell "A22", "2" in cell "B1", "3" in cell "B2" and then click "Ok", the result will be x1 = v0 = 5, x2 = g = 10 (Fig. 2) Fig. 2. Solution of a system of equations. Problem 3. Find the distance traveled by a body thrown at an angle of 30° to the horizontal with an initial velocity of 5 m/s, in a time between 0.1 and 0.3 seconds. Solution. It is known that the velocity of a body thrown at an angle to the horizontal are related to time by the law  sin2 0 22 2 0gtvtgvv  (13) If the velocity is known, then the distance traveled is determined by the integral   2 1 )( t t dttvs (14) By selecting the "Calculating Definite Integrals" section of the program and entering "0.1" in field "A", "0.3" in field "B", "0.001" in field "E" and "Sqr(25+9.8*x^2-49*x)" in the "Function under Integral" field, and then clicking the "Ok" button, we obtain the result s=0.87 (Fig. 3). SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 158 Fig. 3. Calculating Definite Integrals. Problem 4. The dependence of the flight range of a body thrown at an angle to the horizontal with an initial velocity of 5 m/s on the angle of incidence was investigated, and the following results were obtained: , o 30 45 60 75 l, m 2.2 2.55 2.20 1.28 Determine the acceleration due to gravity. Solution. It is known that the flight range of a body thrown at an angle to the horizontal is determined by the formula g v l  2sin 2 0  (15) In this paper, the least-squares method is used to determine the acceleration due to gravity. In this method, to ensure that the experimental results are as close as possible to the theoretically calculated ones, the root-mean-square error 2 1 2)2sin( i N iilA     (16) must be minimal (here A = 2v02/g), that is, the derivative of the root-mean-square error with respect to A must be zero 0)2sin2sin( 1 2 2   ii N iilA A   (17) From the last equation, an expression for determining the acceleration due to gravity is derived     N iii N ii l v g 1 1 22 0 2sin 2sin   (18) SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 159 By selecting the "Least Squares Method" section of the program and entering "4" in the "N" field, "i" in the "Xi" fields, and "li" in the "Уi" fields, and clicking the "Ok" button, we obtain the result g = 9.82, 2 = 8.610-5 (Fig. 4) Fig. 4. Least-squares method. Problem 5. At what angle to the horizontal does a body hit a target, thrown with an initial velocity of 10 m/s, with and without air resistance? Solution: Select the "Choosing an angle for given X, Y, v0" section of the program and enter the values v0 = 10 (m/s), x = 5, y = 1 (m). We determine the launch angle:  = 32.07° (without air resistance) and  = 26.96° (with air resistance, k = 0.1, Fig. 5). Fig. 5. Determining the flight angle (v_0 = 10 m/s, x = 5 m, y = 1 m). By pressing the "Hit Target" button, you can observe how the body hits the target (Fig. 6) both with and without air resistance (k = 0.1, blue line). SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 160 Figure 6. The impact of an object on a target (v0=10 m/s, x = 5 m, y = 1 m) when air resistance is not taken into account (  =32.07о , red line) and when it is taken into account (k=0.1,  =26.96о, blue line). Conclusion Thus, in this work, a program was developed for simulating the motion of a body thrown at an angle to the horizontal, with and without air resistance. A distinctive feature of the program is the ability to quickly and independently input, execute, control, modify, compare, and output data. Highlighting the main advantages of using computer models in physics lessons, it can be noted that using a computer in the classroom significantly increases its effectiveness, speeds up lesson preparation, and allows the teacher to fully express their creativity. Based on the above, it should be noted that the correct use of computer models of physical phenomena promotes nontraditional learning in physics and the development of a physical worldview. Consequently, the use of computer models in physics lessons increases student interest in physics, the quality of learning, and the assimilation of the material. REFERENCES 1. Майер Р. В. Компьютерное моделирование физических явлений. 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