Really weird physics problem, can you help me?

[TrevorRyan]

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?

 

[shreyakmath]

Use the celestial sphere to solve the problem.

 

[tiny-tim]

Hi TrevorRyan!

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

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

 

[shreyakmath]

Yes, an accurate diagram would really benifit

 

[sacscale]

Looks like a trigonometry problem. You are given two sides and the angle between them.

 

[Nessdude14]

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.

 

[sacscale]

Hi TrevorRyan!

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

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

I'd like to see a better description on that first sentence too.

 

[sacscale]

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.

 

[Nessdude14]

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.

 

[sacscale]

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.

 

[Redbelly98]

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.

 

[TrevorRyan]

I always get to the this equation, R+1.7cos0.04625=R, and Have no idea what to do from there.

 

[ehild]

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

 

[TrevorRyan]

wow I am retarded lol. Thx ehild, now i get it