Solving the Tightrope Walker's Shadow Problem

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In summary, the conversation discusses a problem involving a tightrope walker crossing between two buildings with a spotlight shining on them. The first question asks for the speed of the shadow of the walker's feet when they are halfway between the buildings, while the second question asks for the speed of the shadow when the walker is 12 feet away from building B.
  • #1
ayahouyee
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Im stuck on this question! so can someone please please help me? Thank you!

A tightrope is 40 ft above ground between two buildings that are 60 feet apart. A
tightrope walker starts along the rope and walks from building A to building B at
a rate of 2 feet per second. 80 feet above the starting point of the tightrope walker
on building A is a spotlight that is illuminating the tightrope walker as the tightrope
walker is crossing between the two buildings.

(a) How fast is the shadow of the tightrope walker's feet moving along the ground
when the tightrope walker is midway between the buildings?

(b) How fast is the shadow of the tightrope walker's feet moving up the wall of building
B when the tightrope walker is twelve feet away from building B?
 
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  • #2
Re: related rates 2

a) The first thing I would do is draw a diagram:

View attachment 1622

Can you use similarity of triangles to express $s$ as a function of $x$?
 

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FAQ: Solving the Tightrope Walker's Shadow Problem

1. What is the Tightrope Walker's Shadow Problem?

The Tightrope Walker's Shadow Problem is a scientific puzzle that involves calculating the length of a tightrope walker's shadow as they walk across a tightrope. This problem can be solved using principles of geometry and trigonometry.

2. Why is the Tightrope Walker's Shadow Problem important?

The Tightrope Walker's Shadow Problem has real-world applications in fields such as engineering and architecture. Solving this problem can help in designing structures, such as bridges and buildings, that can withstand different lighting conditions and shadows.

3. What are the key principles used to solve the Tightrope Walker's Shadow Problem?

The key principles used to solve the Tightrope Walker's Shadow Problem are trigonometry, specifically the tangent function, and the concept of similar triangles. These principles help in calculating the length of the shadow and the height of the object casting the shadow.

4. Can the Tightrope Walker's Shadow Problem be solved without using math?

No, the Tightrope Walker's Shadow Problem cannot be solved without using math. The problem requires the use of mathematical principles and formulas to calculate the length of the shadow and the height of the object casting the shadow.

5. Are there any real-life examples of the Tightrope Walker's Shadow Problem?

Yes, the Tightrope Walker's Shadow Problem can be seen in everyday situations, such as determining the length of a flagpole's shadow or the height of a tree based on its shadow. It can also be applied in various fields, such as astronomy, where the length of a planet's shadow can reveal its size and distance from the sun.

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