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Dirac

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Dirac.

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- Thread starter Dirac
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- #1

Dirac

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Dirac.

- #2

lurflurf

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let x(t), y(t) be the distance respectively from the wall and floor.Dirac said:

Dirac.

1) relate x and y

2) differentiate the relationship to relate x' and y'

3) find write y(t) in terms of t then find x(t),x'(t),y'(t)

4) use x(ti)=3 to find x'(ti)

- #3

Dirac

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lurflurf said:let x(t), y(t) be the distance respectively from the wall and floor.

1) relate x and y

2) differentiate the relationship to relate x' and y'

3) find write y(t) in terms of t then find x(t),x'(t),y'(t)

4) use x(ti)=3 to find x'(ti)

Could you please do a step-by-step solution

Dirac.

- #4

lurflurf

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No.Dirac said:Could you please do a step-by-step solution

Dirac.

so the ladder, a piece of floor and a piece of wall form a right triangle.

where the legs are x,y and the hypotenus is 5 can you write an equation relating these quantities?

- #5

Dirac

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lurflurf said:No.

so the ladder, a piece of floor and a piece of wall form a right triangle.

where the legs are x,y and the hypotenus is 5 can you write an equation relating these quantities?

Yes, ok but what is x(t)

- #6

HallsofIvy

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hhh79bigo

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- #8

Dirac

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HallsofIvy said:

Yes, I can do it, but I get two solutions for t from

(x^2)=5t-0.25(t^2)

Dirac.

Last edited:

- #9

lurflurf

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x is the distance from the bottom of the ladder to the wall measured along a line along the floor that is perpendicular to the wall.Dirac said:Yes, ok but what is x(t)

y is the distance from the top of the ladder to the floor measured along a line along the wall that is perpendicular to the floor

also I am assuming the wall is perpendicular to the floor

thus we have a right triangle with legs x,y and hypotenus 5

- #10

hhh79bigo

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I get from your values that the velocity of the sliding is 0.333m/s. But don't quote me!

I f you show me your working perhaps i can help

hhh79bigo

- #11

Dirac

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By Pythagoras'

(x^2)+(y^2)=(r^2)

y=5-0.5t

r=5

=>(x^2)=25-(25-5t+0.25(t^2))

=>(x^2)=5t-0.25(t^2)

- #12

Dirac

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Oh ok, done it now.

Dirac.

Dirac.

- #13

lurflurf

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x and y should be positiveDirac said:Yes, I can do it, but I get two solutions for t from

(x^2)=5t-0.25(t^2)

Dirac.

then there is only one solution

There is also an easier way

we know

x*x'+y*y'=0

so

x'=y*y'/x

we know y'=-.5 x=3 y=4 so x' is easy to find

- #14

HallsofIvy

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Dirac said:Yes, I can do it, but I get two solutions for t from

(x^2)=5t-0.25(t^2)

Dirac.

And you STILL haven't shown us what you have done! Don't just give us your (wrong) answer. Show us how you got it.

In fact, your answer makes no sense. The problem does not even ASK you to find t! If you let x be the distance from the wall to the foot of the ladder, the problem asks you to find dx/dt.

Now do what lurflurf suggested to begin with: Draw a picture, look at the right triangle in the picture and write an equation relating the parts of the picture. That will be a "static" equation- your picture is kind of like a snapshot of the sliding ladder. To get a "dynamic" equation (a moving picture) differentiate the entire equation with respect to t (even though there is no t in the equation!)

For the same reason, the answer to hhh79bigo's question is "No, that makes no sense at all- you were not asked to find the time the ladder takes to fall to the floor."

- #15

hhh79bigo

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Forgive me for being ignorant

I apologise I thought that the top of the ladder was 5m of the ground

hhh79bigo

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