Physics: Find the distance along an arc on the surface of the earth that subtends a central angle of 1 minutes (1 minute = 1/60 degree). The radius of the earth is 3960 miles. Round to the thousandths. (3 decimal places)

Find the distance along an arc on the surface

dylanentwistle5197

05.02.2022

1.152 miles

Explanation:

Given: central angle = 1 minute = $(\frac{1}{60}) ^{o}$

radius of the earth = 3960 miles

The length of an arc = $\frac{\alpha }{360^{o} }$ 2 $\pi$ r

where: $\alpha$ is the central angle, and r is the radius.

Thus,

Distance along the arc = $\frac{\alpha }{360^{o} }$ 2 $\pi$ r

Distance along the arc = $\frac{(\frac{1}{60}) ^{o} }{360^{o} }$ x 2 x $\frac{22}{7}$ x 3960

= $\frac{(\frac{1}{60}) ^{o} }{360^{o} }$ x 24891.4286

= 1.1524

The required distance along an arc is 1.152 miles.

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