![]() ![]() From the equation s = vcos(θ)t, and t = 2vsin(θ)/g. Rearranging the equation for finding t, vsin(θ)/g = t, this is the time it takes to reach its maximum height, so we multiply by 2 to get the total time for it to reach the maximum height and return back to the initial height. At maximum height, the vertical velocity(vsin(θ)) is reduced to zero, so the equation should give vsin(θ) - gt = 0. Knowing that the time it takes for the projectile to reach the maximum height from its initial height is the same as the time it takes to fall from the maximum height back to its initial height. So the issue is to find time(t), the time is affected by the vertical component of velocity and the acceleration due to gravity(g). Knowing that the horizontal velocity = vcos(θ), so we can get the horizontal distance(s) = horizontal velocity x time, s = vcos(θ)t.Ģ. Hence the optimal angle of projection for the greatest horizontal distance is 45° because sin(90) = 1, and any other angle will result in a value smaller than 1.ġ. I tried to drive a formula, ending up having the horizontal distance traveled = v^2sin(2θ)/g. : Added Perfect Card Shuffling (In Fun Stuff).For the question of comparing the horizontal distance traveled of different initial angles of projection. : Added Image Formation with Convex Lenses (In Light). : Added Electron Charge to Mass Ratio Lab (In Electricity and Magnetism). Please feel free to use any of the content on this site for non-profit educational purposes. To browse or search for pre-made math and physics simulations (including those used on this site) and for more information about the software please visit their website: Permissions GeoGebra is a free program that makes it very easy to create animations and simulations for anyone with a good understanding of math or physics. Most of the animated illustrations and all of the interactive simulations on this site were created using the wonderful GeoGebra software. Please click my name above to send me feedback about these simulations or suggestions for new simulations I could create. I retired after teaching high school physics for 27 years, and AP Physics for 25 years. Content will be added as time allows.Īll of the content on this site was created by me, Tom Walsh. It is a work in progress, and likely always will be. The oPhysics website is a collection of interactive physics simulations. Select a simulation from one of the above categories or click on a category to see descriptions of the simulations for that category.
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