the minute hand of a clock is 5 cm long. what is the linear velocity, in centimeters per minute, at the tip…

Explanation:

Step1: Determine the circumference formula

The distance traveled by the tip of the minute - hand in one hour (60 minutes) is the circumference of a circle. The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius of the circle. Here, the length of the minute - hand is the radius, so $r = 5$ cm. $C=2\pi r=2\pi\times5 = 10\pi$ cm.

Step2: Calculate the linear velocity

The minute - hand makes one full revolution (covers a distance equal to the circumference) in 60 minutes. The linear velocity $v$ is given by the formula $v=\frac{d}{t}$, where $d$ is the distance traveled and $t$ is the time taken. $v=\frac{10\pi}{1}\text{ cm/min}\approx 31.42$ cm/min.

Answer:

$31.42$