This was the bonus question on my physics exam

Lord_Tryzalot
Lord_Tryzalot

This was the bonus question on my physics exam. The answer I gave was around 48m. Can some physics fags get the answer right / call me a brainlet?

You drop a rock in a well, it takes 3 seconds until to hear it. Given that the speed of sound is 343m/s, what is the height of the well?

Boy_vs_Girl
Boy_vs_Girl

343 m/s * 3 s = 16890 m
glad I could hepl

MPmaster
MPmaster

@Boy_vs_Girl
but you also have to account for how long the rock takes to fall

King_Martha
King_Martha

@MPmaster
I simplified the problem by assuming that I knew the correct answer

Spamalot
Spamalot

@Lord_Tryzalot
why did you answer 48?

shouldnt it just be 343*3=1029

1029 metres

girlDog
girlDog

@MPmaster
how long does it take for the rock to fall?

Evil_kitten
Evil_kitten

Does the 3 seconds account for the dropping of the rock

viagrandad
viagrandad

@Spamalot
Well, I figured, since its in free fall, that it would take some time to reach the bottom, and that maybe, since sound speed is so quick, that the distance covered by the time it takes to reach the bottom is small such that sound reaches your ear quick?

I can give a detailed procedure of what I did, though.

happy_sad
happy_sad

>>9228408
faggot OP didnt specify how heavy the rock was. psh go back to school, kid

SomethingNew
SomethingNew

@viagrandad
certain elements fall faster or slower than others. its a trick question from the start. i think your teacher is a troll

5mileys
5mileys

@Evil_kitten
Yes, I assumed this.
@viagrandad
To clarify further, the time it takes to reach bottom I assume to be less than 3 seconds.

cum2soon
cum2soon

@happy_sad
Top kek, Do you just work on problems without reading and thinking about what it's asking?

takes2long
takes2long

y = -0.5g(t)^2
y = 343 (t')
t+t' = 3

Now do algebra.

w8t4u
w8t4u

@happy_sad
We're using a simplified model where the body is just a point, mass isn't taken into account.
@SomethingNew
What about the experiment on the moon (feather vs cannonball)?

Bidwell
Bidwell

I got 40.6 meters, but take this with a grain of salt as I havent done physics in years.

let d be the depth of the well, s be the time the rock spent falling and s be the time the sound spent moving. then d = 1/2 * 9.8 * r^2, d = 343 * s, 3 = s + r. solving gives 40.6 as d.

iluvmen
iluvmen

@Bidwell
oops r is the time the rock spent falling, not s

likme
likme

g = 10
after 2s it's fallen 30 m
but 30/343 is much less than 1
after 2.5 s it's fallen 42.5 m
42.5/343 is less than .5
after 2.75 s its fallen 52.5 m
52.5/343 again not .25
after 2.9 s it's fallen
57 m
57/343 is greater than .1 m
back to 2.8 s fallen 54 m
54 / 343 < .2
so try 2.85 s....

can someone smarter than me come up with a relationship?

kizzmybutt
kizzmybutt

@Bidwell
Ay = g and not -g?

Poker_Star
Poker_Star

@likme
If I remember correctly, that t was near the t I plugged into y = -.5g(t^2)

Playboyize
Playboyize

@kizzmybutt
d is the depth of the well, it must be a positive value

Techpill
Techpill

@likme
yeah I'm wrong you have to integrate the velocity gt to find the distance

gt^2/2 = c
then (3-t)343 = c

another user already provided this

TreeEater
TreeEater

@Techpill
so (3-(2c/g)^.5)343=c
@Bidwell
is right

Carnalpleasure
Carnalpleasure

@Bidwell
Fuck, this makes most sense.
Lmao I remember doing a quadratic formula and getting a negative time (which yielded that 47m)
Thanks user.

Flameblow
Flameblow

@Carnalpleasure
It sounds like you did d = -1/2 ..., which gives d = -48.
Really close and frustrating lol. You need either be really, really attentive with your choice of coordinates (which would have caused you to correctly add a negative to the other equation) or rely on good physical intuition. I'm not sure what insight lead me to realize you could ignore signs, let d be the length of the well and figure out how long it would take to fall and echo across that length, but over time you start to intuit these things. I studied physics for six years so I've had time to build up that intuition.

WebTool
WebTool

@Boy_vs_Girl
343 / s

CouchChiller
CouchChiller

@w8t4u
We're using a simplified model where the body is just a point, mass isn't taken into account.
then how does sound propagate if nothing has masses

the prof is a retard.

idontknow
idontknow

There might be a smarter way to do it, but this is how I reasoned it out.

After the rock is dropped, at some time, tf, it reaches the bottom of the well, h. The distance the rock travels should be y=-(g*t^2)/2

So plugging in our known tf and h: h=-(g*tf^2)/2

We know that after the rock reaches the bottom of the well, the sound travels up at 343 m/s, unaffected by gravity and moving at a constant velocity, we know that we can just use d = v*t the distance traveled being h, the velocity being the speed of sound, and t being the time difference between 3 seconds and tf, note that because the rock and the sound travel in opposite directions you need to account for the sign difference, so just through in a negative sign. h = - 343 * (3-tf)

Setting the two equations equal to one another, you have a quadratic, one of the times you get is tf = 2.8812820, plug that back in to the y=-(g*t^2)/2 and you get 40.7202612 m

I think I solved this right, and I hope more work was follow-able.

Techpill
Techpill

@Lord_Tryzalot
X-Xo=Xo+Vo*t+at^2/2

use this feggit

Garbage Can Lid
Garbage Can Lid

@CouchChiller
Too bad, but you are a brainlet

Evil_kitten
Evil_kitten

@idontknow
@Techpill
Solved it before seeing your posts but yeah, here's the reasoning
pic related

Emberfire
Emberfire

@likme
g=10

RavySnake
RavySnake

@Lord_Tryzalot
implies you should ignore air resistance
then gives you the speed of sound in air
Pig disgusting, hang your professor.

Nude_Bikergirl
Nude_Bikergirl

@idontknow
yeah and what is the mass of the thing

Garbage Can Lid
Garbage Can Lid

@Lord_Tryzalot
first year physics was fun, except for lab
lab was chinsey as fuck

Evil_kitten
Evil_kitten

@Emberfire

implying engineers use g = 10 m / s^2 instead of g = 32 ft / s^2

askme
askme

tyson chicken question. the height of the well is exactly 0. level water is the reference

askme
askme

I assume you know that [math]D = A/2 * T^2[/math]
or if you rearrange the equation [math]T = \sqrt{D/(A/2)}[/math]

so your equation is [math]\sqrt{D/(10/2)} + D/343 = 3[/math]
I don't know calculus very well so I can't do this

Methshot
Methshot

@Nude_Bikergirl
5

likme
likme

@Ignoramus
What programming language is this?

TreeEater
TreeEater

@Lord_Tryzalot
Is air resistance negligible?

Firespawn
Firespawn

@likme
g=10
Engineer spotted

BlogWobbles
BlogWobbles

@Lord_Tryzalot
physicist post doctorate here

easy.

how heavy is the rock brainlet so I can calculate how fast does it fall.

TechHater
TechHater

@BlogWobbles
24 mg

Stupidasole
Stupidasole

The derivative of 343m^3 is 1029m^2. 1029 - 343 is 686. The answer is 686

Ignoramus
Ignoramus

@Stupidasole
the derivative of a number as a function is 0

TalkBomber
TalkBomber

d = .5*g*t^2; t1=sqrt(2d/g)
t2=d/v
both times add to 3 seconds
3 = sqrt(2d/9.81)+d/(343)
9 -6d/343+d^2/343^2=2d/9.81
9-d(6*9.81+686)/(343*9.81) + d^2/343^2=0
quadratic equation
d = 40.71 meters

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