Ladder and bridge problem

T

TheAngryMathStudent

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Joined
Feb 28, 2014
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4
Hello

I can't work out this problem. I have no idea where to start, and it's an assignment due soon. Can someone please help me with a step-by-step solution or atleast partial solution?

1)

6,5m ladder resting up against a wall. The lader gets pulled away from the wall (while still resting on it) at a speed of 0,5 m/s.

At what speed does the ladder move downward when it's 6m up on the wall.

2)
They're building a bridge to an island.

The coastline of mainland have the function: y-0
The costline of the island have the function: y-f(x)-(1/4)*cost(x) + (x/8)
The bridge is gonna get built in a interval where x is [0, pi]

Fin the spot on (x, yIsland) on the island and (x,0) on mainland so that the bridge is as short as it can be. Explain why the bridge is shortest here.


Anyone who can help me out/nudge me in the right direction?

Any help is greatly appreciated.
 
TheAngryMathStudent said:
Hello

I can't work out this problem. I have no idea where to start, and it's an assignment due soon. Can someone please help me with a step-by-step solution or atleast partial solution?

1)

6,5m ladder resting up against a wall. The lader gets pulled away from the wall (while still resting on it) at a speed of 0,5 m/s.

At what speed does the ladder move downward when it's 6m up on the wall.

2)
They're building a bridge to an island.

The coastline of mainland have the function: y-0
The costline of the island have the function: y-f(x)-(1/4)*cost(x) + (x/8)
The bridge is gonna get built in a interval where x is [0, pi]

Fin the spot on (x, yIsland) on the island and (x,0) on mainland so that the bridge is as short as it can be. Explain why the bridge is shortest here.


Anyone who can help me out/nudge me in the right direction?

Any help is greatly appreciated.
Click to expand...
Hint for #1

Draw a sketch of the situation

Use Pythagorian theorem.

Differentiate to get the speeds of two tips of the ladder.

and continue....

Hint for #2

Sketch the situation with x-axis as your coast-line of mainland.

Draw the coast line of the island as the given function

Now derive function that describes distance of any point on the coastline of the island to the x-axis (mainland coast-line)

and continue....

Please share your work with us .

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting
 
x^2 + y^2 = L^2

2x dx/dt + 2y dy/dt = 0

y dy/dt = -x dx/dt

dy/dt
----- = -x/y
dx/dt


dy/dt
-------- = 2,5/6 (6 is m up on the wall and 2,5 is how far (x) the ladder has been drawn out?)
0,5


So dy/dt = 0,2083? Is this correct?
 
TheAngryMathStudent said:
x^2 + y^2 = L^2

2x dx/dt + 2y dy/dt = 0

y dy/dt = -x dx/dt

dy/dt
----- = -x/y
dx/dt


dy/dt
-------- = 2,5/6 (6 is m up on the wall and 2,5 is how far (x) the ladder has been drawn out?)
0,5


So dy/dt = -0,2083? Is this correct?
Click to expand...

The negative sign is important - indicating that as 'x' increases, 'y' decreases.
 
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