Please answer part B of the question The time to sunset can be estimated by hold

Question

Please answer part B of the question

The time to sunset can be estimated by holding out your arm, holding your fingers horizontally in front of your eyes, and counting the number of fingers that fit between the horizon and the setting Sun. (a) What is the angular speed, in rad/s, of the Sun's apparent circular motion around the Earth? Give answer in scientific notation times 10 rad/s 7.3 Part 2 out of 3 (b) Estimate the angle subtended by one finger held at arm's length. An estimate for an arm-length is 0.85 m, and for a finger width an estimate is 2.3 cm. rad

Explanation / Answer

The earth turns 2 Pi() radians in 24 hours which is 24 * 60 * 60 sec
So the angular rate is 2Pi()/(24*60*60) radians per sec. ( 7.3 * 10 ^ -5 rads per sec)
This is the apparent rate of the sun moving around the earth approximately.

2cm at 100 cm distance subtends an angle of 2/100 = 0.02 radians


w = theta / time where w is the angular velocity and theta is the angle subtended.
w = 7.3 * 10 ^ -5
theta = 0.02

so time = theta/w
= 0.02 / (7.3* 10 ^ -5)
=274 secs or 4 and one half minutes approx.

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