Compact Disc. A compact disc (CD) stores music in a coded pattern of tiny pits 10^-7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. (b) The maximum playing time of a CD is 74.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line?

Video transcript

Hey everyone today, we're dealing with some problems regarding the constant linear speed. So we're told that a printing hand is constant linear printing speed of 1. m/s. Now the printing head spins in a circle as a princess circular pattern on a piece of piece of fabric. The inner radius of the pattern is 22 cm while the outer radius is cm. If the printer takes 42 minutes to complete the pattern, what is the length of the printed pattern when it is stretched into a straight line. So let's think about this. We are being asked to find the length of the printed pattern. So we're being asked to find the length or the distance traveled. And we are given a constant linear speed. So with that we can actually use the formula V. X. Multiplied by T. Because remember distances simply velocity times time. Now substituting in our values, we get that v. X. is equal to 1.8 m 1.8 m/s and the time. Well we need it in seconds but are given minutes. So let's expand that. It's 42 minutes And we can recall that we have 60 seconds for every one minute. So our minutes will cancel out. And we can convert that Giving us a final answer of four point or 4536 m. No this aligns with answer choice D. Meaning that the distance or the length of the printed pattern when it is stretched in a straight line is 4536 m or 4.5 kilometers, It's really long. I hope this helps, and I look forward to seeing you all in the next one.