#Help! no clue how this is supposed to be solved...

101 messages · Page 1 of 1 (latest)

vague wave
gusty sluice
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,rccw

north runeBOT
gusty sluice
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looks like it gives the solution there

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are you having trouble understanding it? Or do you want some hints to try to figure it out yourself without being told the full solution?

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if the former, which part are you having trouble with?

vague wave
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it makes no sense

vague wave
gusty sluice
vague wave
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right triangle comes to mind

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and then a smaller triangle

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in the bigger one

gusty sluice
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what you need to do is find an equation for the length of the shadow in terms of the distance the man has walked

vague wave
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ok so

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if distance travelled is d

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and shadow length is x

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then i need to find an equation between d and x?

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is that what ur sayig

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ng

gusty sluice
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yes

vague wave
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hmmmm

gusty sluice
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then you differentiate that equation with respect to time

vague wave
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how would i do that

gusty sluice
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d/dt both sides

vague wave
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its 2 bases of right triangles

gusty sluice
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you know that dd/dt = 6 m / min

vague wave
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no the step before

gusty sluice
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can you draw the diagram and send an image of it?

vague wave
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book diagram for reference

image.png
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so

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idk

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what next

gusty sluice
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distance traveled = x + y

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shadow length = y

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relate the two

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(hint: think about similar triangles)

vague wave
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huh

vague wave
gusty sluice
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the triangles ABE and CDE have the same angles (are similar)

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meaning that the ratios between the corresponding sides are the same

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e.g. BE : DE = AE : CE

vague wave
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the ratio of be to de is the same as ae to ce?

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let me think about this

gusty sluice
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ABE is CDE "scaled up"

vague wave
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OH i get it

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the side ratios have to match up

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because its the same triangle but bigger

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and the scalar has to be constant

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so the ratios are same

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but that helps...how

gusty sluice
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remember we want to relate AE with CE

vague wave
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hmmm

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the ratios ae : ce are the same as bd : de

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and also

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ab : dc = ae:ce?

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ab/dc = ae/ce

gusty sluice
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yes

vague wave
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6/2 = x+y / y

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3 = x+y/y

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3y = x+y

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3y-y = x

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2y = x

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y = x/2

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mm

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and then?

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so the length of the shadow is half the distance between the guy and the pole

gusty sluice
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so AE = 3 CE

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which should make sense because ABE is just CDE scaled up by a factor of 3

vague wave
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oh

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okay

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and then we differentiate both?

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but why

gusty sluice
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2 x = y

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what we want is dy/dt

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we know dx/dt = 6 m/min

vague wave
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we know dx/dt right

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oh

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right

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so

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2y = x

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2 dy/dt = 6

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dy/dt = 3

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!

gusty sluice
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yep, that's it lol

vague wave
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now that the maths is done

gusty sluice
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the shadow length is just a constant proportion of the distance the guy has traveled

vague wave
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let me review what we did

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so

gusty sluice
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so their derivatives are as well

vague wave
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the shadow is some constant times the distance between man and pole

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we need to find the constant so we can write the equation

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ky = x

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and then diff. both sides

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this makes so much mmore sense now lol thx

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@gusty sluice appreciate you being patient with me, btw can you perhaps help me with another problem if you have the time!

gusty sluice
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np! You should ask your question in another thread, and I'll take a look at some point if nobody beats me to it

vague wave
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okayge

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