Impact velocity from given height Onedimensional motion Physics Khan Academy
What I want to dothis tutorialis answer an ageold question, or at least an interestingquestion to me. And the question is, let'ssay I have a ledge here I have a ledge orcliff, or maybe this is a building of some kind. And let's say it has height, h. So let's say it has a heightof h, right over here.
And what I'm curious about isif I were to either Let's say that this is me overhere, so this is me. If I were to eitherjump, myself that's not recommendedfor very large h's. Or If I were to throw something,maybe a rock off of this ledge, how fast wouldeither myself or that rock be going right beforeit hits the groundé And like all of theother tutorials we're
doing on projectilemotion right now, we're going to ignoreair resistance. And for small h's andfor small velocities, that's actually reasonable. Or if the objectis very aerodynamic and is kind of dense,then the air resistance will matter less. If it's me kind of bellyflopping from a high altitude,
then the air resistancewill start to matter a lot. But for the sake of simplicity,we're going to assume no air. Or we're not goingto take into effect the effects of air resistance. Or we could assumethat we're doing this on an Earthlike planetthat has no atmosphere. However you want to do it. So let's just thinkabout the problem.
And just so you know,some of you might say, that's not realistic. But this actually would berealistic for a small h. If you were to jump off of theroof of a onestory building, air resistance will notbe a major componentdetermining your speed if. It was to be a much largerbuilding, then all of a sudden it matters.
And I don't recommend youdo any of these things. Those are all verydangerous things. Much better to doit with a rock. So that's actually the examplewe're going to be considering. So let's just thinkabout this a little bit. We want to figureout So at the top, right when thething gets opped, right when therock gets opped,
Projectile height given time Onedimensional motion Physics Khan Academy
Let's say you and I areplaying a game where we're trying to figure out how high aball is being thrownthe air or how fast that we'rethrowing that ballthe air. And what we do isone of us has a ball and the other one hasa stopwatch over here. So this is my best attempt. It looks more like a than a stopwatch,
but I think you get the idea. And what we do is oneof us throws the ball, and the other one times howlong the ball isthe air. And then what wedo is we're going to use that time inthe air to figure out how fast the ball wasthrown straight up, and how long it wastheair and how high it got. And there's going to be oneassumption I make here
and frankly, thisis an assumption that we're going to makein all of these projectile motiontype problems is thatair resistance is negligible. And for something like ifthis is a baseball, or something like that, that's apretty good approximation. So we're not going toget the exact answer. And I encourage you toexperiment on your own
to see what air resistance doesrelative to your calculations. But we're going to assumefor this projectile motion and really all ofthe future ones or at leastthebasic physics playlist we're going to assume thatair resistance is negligible. And what that does forus is that we can assume that the time for the ballto go up to its peak height is the same thing as the timethat it takes to go down.
If you look atthis previous tutorial where we plotteddisplacement versus time, you see after 2 seconds the ballwent from being on the ground or I guess the thrower's handall the way to its peak height. Andthe next 2 seconds, ittook that same amount of time to go back down to theground, which makes sense. Whatever theinitial velocity is, it takes half thetime to go to 0.
And it takes thatsame amount of time to now be acceleratingin the downward direction back to that samemagnitude of velocity but nowthedownward direction. So let's play aroundwith some numbers here just so we get a littlebit more of a concrete sense. So let's say I throwa ballthe air. And you measure,using the stopwatch,