Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-A pendulum of length $17.0$ inches swings $1 ^ { \circ } 6 ^ { \prime }$ to each side of its vertical position. What is the length (to the nearest hundredth of an inch) of the arc through which the end of the pendulum swings?
A) $0.45 \mathrm { in }$.
B) $0.65$ in.
C) $0.55$ in.
D) $0.35$ in.

Question

Quizplus · Accepted Answer

The length of the arc can be calculated using the formula for the arc length of a circle, $s = r\theta$, where $s$ is the arc length, $r$ is the radius, and $\theta$ is the angle in radians. First, convert the angle from degrees and minutes to radians: $1^\circ 6' = 1^\circ + \frac{6}{60}^\circ = 1.1^\circ$. Since there are $2\pi$ radians in $360^\circ$, $1.1^\circ = \frac{1.1}{360} \times 2\pi$ radians. The length of the pendulum is $17.0$ inches, which acts as the radius ($r$). Substituting these values into the formula gives the arc length. Since the pendulum swings to each side, the total angle is $2 \times 1.1^\circ$, but for the calculation of a single side, we use $1.1^\circ$ converted to radians. The calculation will yield a result close to $0.65$ inches, considering the conversion from degrees to radians and the use of the pendulum's length as the radius.

Assume That the Cities Lie on the Same North-South Line 17.017.017.0

Assume That the Cities Lie on the Same North-South Line $17.0$