Suppose that, while lying on a beach near the equator watching the Sunset 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?
The radius of the earth is
The height of the person h = 1.70 m
Time elapsed t = 11.1 sec ,
Considering the projection of the earth is nothing more thana circle. A person standing in the center of the circle can be seen as a line h. Drawing the tangent to the circle from the line h it forms a rectangular triangle. Therefore, using the Pythagorean Theorem, the radius of the earth can be calculated.
When the person stands up, his line-of-sight changes. Find the angle using these two different lines of sight. Using this value of and the time in which this change took place, it is possible to find the radius of the earth.
From Pythagorean Theorem,
Here,h is very small as compared to r, so neglecting higher terms of h,
Convert 24 into seconds.
1 hr = 3600 sec
Earth takes 24 hrs for one complete rotation, that is, 360 degree
So, for t = 11.1 s it takes θ degrees,
Thus, the angle is
From the figure, it can be written that,
Squaring both the sides,
Now substitute the value of from equation (i) to find the equation for .
Substitute the values in equation (iii) to calculate the radius of the earth.
Thus, the radius of the earth is
One molecule of water contains two atoms of hydrogen and one atom of oxygen. A hydrogen atom has a mass of and an atom of oxygen has a mass of , approximately. (a) What is the mass in kilograms of one molecule of water? (b) How many molecules of water are in the world’s oceans, which have an estimated total mass of ?
Question: For about 10 years after the French Revolution, the French government attempted to base measures of time on multiples of ten: One week consisted of 10 days, one day consisted of 10 hours, one hour consisted of 100 minutes, and one minute consisted of 100 seconds. What are the ratios of (a) the French decimal week to the standard week and (b) the French decimal second to the standard second?
Two types of barrel units were in use in the 1920s in the United States. The apple barrel had a legally set volume of 7056 cubic inches; the cranberry barrel, 5826 cubic inches. If a merchant sells 20 cranberry barrels of goods to a customer who thinks he is receiving apple barrels, what is the discrepancy in the shipment volume in liters?
An iceboat is at rest on a frictionless frozen lake when a sudden wind exerts a constant force of 200 N, toward the east, on the boat. Due to the angle of the sail, the wind causes the boat to slide in a straight line for a distance of 8.0 m in a direction 20 north of east. What is the kinetic energy of the iceboat at the end of that 8.0 m?
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