Blog three: Heads Up, We're Coming Down

"Talk to the hand."

This lunchbox part of a dramatic reenactment.

Pop quiz! What do you get when you combine my accident-prone friend, a metal lunch box, and a distracted high school student?

You get an announcement in the Daily Bulletin asking students to please stop putting things on the railing of second floor I-building.

Good times, man. Good times.

Alright, it wasn't really good times.

But, back to physics. The lunchbox was balanced on the railing while the absent-minded student was diddling about in her locker. She (while wearing her gigantic school-issued backpack) then backed up and it was all over bar the blood and out-freaking.

In other words, it was launched horizonally, which incidentally makes these numbers a lot easier to calculate!

There is no way this could possibly go wrong.

As we're all aware, the horizontal and vertical components of a vector may be treated separately. I have a tape measure, so let's get started.

We already know

initial vertical speed = 0 m/s

vertical acceleration = -9.8 m/s/s

and I went and found out that vertical displacement = -3.27 m

So now we can find out time because (say it with me, everybody!)

displacement = initial velocity*time + 0.5*acceleration*time*time

So time = 0.58 s

And we (and by "we" I mean "I," obviously) can then figure out the horizontal velocity using the same equation, because my tape measure says that the lunchbox went 0.80 m in the horizontal direction.

horizontal velocity = 1.38 m/s

Pretty good booty bump, yes?

And finally, we can find out the lunchbox's final vertical velocity (how fast it was going when it creamed her).

instantaneous velocity = initial velocity + acceleration*time

instantaneous vertical velocity = -5.73 m/s

She's going to want to put some ice on that.

PS: I used three pictures Ms C. Do I get, like, bonus points? 

Total distance traveled and displacement are not the same thing.

Yes, it's one continuous line.

So last night I was drawing (as I am wont to do) and I ended up with, well... this.

And I thought, hey, cool. 

And then I thought, you know what this illustrates really well? The difference between distance traveled and displacement.

Total distance is exactly what it says on the tin. It's the distance that you have traveled, regardless of direction (toward or away from the origin).

Displacement does take into account direction of travel, and is the shortest distance between your starting point and end point. (I've circled both points in red on the off chance that you can't figure out where each one is.)

As long as I'm applying physics to doodles, I might as well add that my marker speed was pretty much constant, but my velocity was not. Speed is distance traveled over time; velocity measures speed and direction. I made a lot of crazy little turns there. (I mostly tried to avoid looks and crossing over previously established lines, though. It would have made it look confusing.) In fact there were velocity changes out, as I believe the scientific term is, the wazoo.

If you wanted to calculate my average velocity, you'd take the distance between the handily-circled points and divide it by the time it took me to draw this (a long time). If you wanted to find my average speed, you'd have to find my total distance and then divide it by time.