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Benacka, Jan – Physics Education, 2017
This paper gives an account of an experiment in which thirty-three high school students of ages 17-19 developed spreadsheet numerical models of satellite and space probe motion. The models are free to download. A survey was carried out to find out the students' opinion of the lessons.
Descriptors: Science Instruction, High Schools, Secondary School Science, Physics
Benacka, Jan – EURASIA Journal of Mathematics, Science & Technology Education, 2016
The article gives an account of an experiment in which sixty-eight high school students of age 16 - 19 developed spreadsheet applications that simulated fall and projectile motion in the air. The students applied the Euler method to solve the governing differential equations. The aim was to promote STEM to the students and motivate them to study…
Descriptors: High School Students, STEM Education, Mathematical Models, Spreadsheets
Benacka, Jan – Physics Education, 2015
This paper gives the solution and analysis of projectile motion in a vacuum if the launch and impact heights are not equal. Formulas for the maximum horizontal range and the corresponding angle are derived. An Excel application that simulates the motion is also presented, and the result of an experiment in which 38 secondary school students…
Descriptors: Motion, Science Instruction, Physics, Scientific Principles
Benacka, Jan – Physics Education, 2015
This paper provides the formula for the elevation angle at which a projectile has to be fired in a vacuum from a general position to hit a target at a given distance. A spreadsheet application that models the trajectory is presented, and the problem of finding the points of shot and impact of a projectile moving in a vacuum if three points of the…
Descriptors: Spreadsheets, Science Instruction, Physics, Motion
Benacka, Jan – International Journal of Mathematical Education in Science and Technology, 2010
This note gives the analytical solution to projectile motion with quadratic drag by decomposing the velocity vector to "x," "y" coordinate directions. The solution is given by definite integrals. First, the impact angle is estimated from above, then the projectile coordinates are computed, and the trajectory is graphed at various launch angles and…
Descriptors: Motion, Spreadsheets, Equations (Mathematics), Mathematical Formulas
Benacka, Jan – International Journal of Mathematical Education in Science and Technology, 2009
This note gives a power series solution to the pendulum equation that enables to investigate the system in an analytical way only, i.e. to avoid numeric methods. A method of determining the number of the terms for getting a required relative error is presented that uses bigger and lesser geometric series. The solution is suitable for modelling the…
Descriptors: Motion, Geometric Concepts, Equations (Mathematics), Mathematics Instruction
Benacka, Jan; Stubna, Igor – International Journal of Mathematical Education in Science and Technology, 2009
This note gives the solution to the motion of a perfectly hard ball that was launched against a perfectly hard inclined plane. The solution comprises recurrent formulas that give the parts of the trajectory between the impacts, which are parabolas. In the upward part of the motion, the parabolas become higher and narrower, in the downward part…
Descriptors: Energy Conservation, Physics, Motion, Spreadsheets