Really weird physics problem, can you help me?

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Homework Help Overview

The problem involves calculating the radius of the Earth based on the time it takes for the Sun to set as observed from a height of 1.70 m. The context is set near the equator, and the scenario includes the use of a stopwatch to measure the elapsed time until the Sun disappears again after standing up.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of the celestial sphere and trigonometry to approach the problem. There are questions about the sides and angles involved, particularly regarding the unknown radius of the Earth and the relationship between the height of the observer and the geometry of the situation.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the original poster's attempts and encouraging the sharing of diagrams. Some have pointed out potential issues with the equations being used, while others emphasize the need for a better understanding of the geometric relationships involved.

Contextual Notes

There is a note from a moderator requesting that the original poster respond with their attempts before further hints are provided. This indicates a structured approach to the discussion, focusing on the original poster's engagement with the problem.

TrevorRyan
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Suppose that, while lying on a beach near the equator watching the Sun set over a calm ocean, you start a stopwatch just as the top of the Sun disappears. You then stand, elevating your eyes by a height H = 1.70 m, and stop the watch when the top of the Sun again disappears. If the elapsed time is t = 11.1 s, what is the radius r of Earth?
 
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Use the celestial sphere to solve the problem.
 
Hi TrevorRyan! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:

(you'd better start with a really good diagram!)
 
Yes, an accurate diagram would really benifit
 
Looks like a trigonometry problem. You are given two sides and the angle between them.
 
sacscale said:
Looks like a trigonometry problem. You are given two sides and the angle between them.

How so? You can figure the angle that the Earth rotates in the problem, but you aren't given the sides that enclose that angle.
 
tiny-tim said:
Hi TrevorRyan! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:

(you'd better start with a really good diagram!)

I'd like to see a better description on that first sentence too.
 
Nessdude14 said:
How so? You can figure the angle that the Earth rotates in the problem, but you aren't given the sides that enclose that angle.

One side is the radius the other is the radius plus 1.70m.
 
sacscale said:
One side is the radius the other is the radius plus 1.70m.

Those sides aren't given, the radius of the Earth is an unknown in this problem. If you try to apply the law of cosines, you get 2 unknowns and only one equation.
 
  • #10
Nessdude14 said:
Those sides aren't given, the radius of the Earth is an unknown in this problem. If you try to apply the law of cosines, you get 2 unknowns and only one equation.

At the tangent to the surface is a right angle.
 
Last edited:
  • #11
Moderator's note

At this point, please let TrevorRyan respond with an attempt toward working out the problem, in accordance with our forum guidelines on Homework Help. Please do not post further hints and help until we here from the OP.
 
  • #12
I always get to the this equation, R+1.7cos0.04625=R, and Have no idea what to do from there.
 
  • #13
Add parentheses at the proper places? Your equation means that 1.7 cos0.04625=0 which is obviously wrong.

For better understanding, I attach the missing figure. One sees the sunset when the ray arriving to the eye from the sun is tangent to the Earth.

ehild
 

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  • sunset2.JPG
    sunset2.JPG
    13.6 KB · Views: 456
  • #14
wow I am retarded lol. Thx ehild, now i get it
 

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