Question

1. the earth rotates about its axis once every 23 h 56 min 4 s, and the radius of the earth is 3960 mi. find the linear speed of a point on the equator in mi/hr.

Explanation:

Step1: Convert rotation time to seconds

First, convert 23 hours 56 minutes 4 seconds to seconds.
$23\times60\times60 + 56\times60+4=82800 + 3360+4 = 86164$ seconds.

Step2: Calculate the circumference of the Earth at the equator

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 3960$ miles, $C=2\pi\times3960$ miles.

Step3: Calculate linear - speed

Linear speed $v=\frac{d}{t}$. Here, $d = C = 2\pi\times3960$ miles and $t = 86164$ seconds. To convert the speed to miles per hour, we know that there are 3600 seconds in an hour.
$v=\frac{2\pi\times3960}{86164}\times3600\approx1037.5$ miles per hour.

Answer:

Approximately $1037.5$ mi/hr