How to Solve Projectile Motion Problems in One or Two Lines

AI Thread Summary
Projectile motion problems can be efficiently solved in one or two lines by prioritizing key parameters over time. The discussion introduces two main equations that connect five essential variables: horizontal displacement, vertical displacement, initial horizontal velocity, initial vertical velocity, and final vertical velocity. By treating these variables as a system of equations, one can derive the time of flight using the formula Δx/v0x. Additionally, three auxiliary shortcut equations are provided to streamline the process of identifying parameters. This method offers advantages over traditional approaches, making it a valuable strategy for solving projectile motion problems.
kuruman
Science Advisor
Homework Helper
Education Advisor
Insights Author
Gold Member
Messages
15,773
Reaction score
8,955
Introduction
We show how one can solve most if not all, introductory-level projectile motion problems in one or maybe two lines. To this end, we forgo convention.  We demote clock time ##t## to a parameter of secondary importance and ditch the independence of motion in the vertical and horizontal directions.
Starting from the first principles, we develop two primary equations that relate five “basic” parameters to each other: ##\Delta x##, ##\Delta y##, ##v_{0x}##, ##v_{0y}## and ##v_y## (standard definitions).  We view the solution of projectile motion problems as equivalent to solving a system of five equations with the five basic parameters as the five unknowns.  Once the system is solved, the time of flight, if one must have it, is just the ratio ##\Delta x/v_{0x}##.
To sharpen the implementation of the primary equations, we recombine them to derive three auxiliary shortcut equations that facilitate the identification of equation parameters with given variables.  Finally, we...

Continue reading...
 
Last edited by a moderator:
  • Like
Likes Dale, neilparker62, BvU and 1 other person
Physics news on Phys.org
This is a nice approach. It does seem to have some advantages over the standard approach.
 
Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two speeds, is it also possible to state that the average speed over this 2L-kilometer stretch can be obtained as a weighted average of the two speeds? Best regards, DaTario
This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
Back
Top