Distance Traveled by a Minute Hand Suppose the tip of the minute ...

Question

Distance Traveled by a Minute Hand Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand. Leave answers as multiples of  π .                                                                                                                                                                                                                                                                                                                                        
                                                                                                                                                                                                                                                                                                                                                                                        
  ​​30 min

Accepted Answer

Welcome back. I am so glad you're here. We're asked to calculate the distance covered by the minute hand of a clock for the following duration. If the distance of the tip of the minute hand from the center of the clock is six centimeters, write your answer in terms of pie. Our duration is for 50 minutes. Our answer choices are answer choice, a 20 pi centimeters. Answer choice B 10 pi centimeters, answer choice, C five pi centimeters and answer choice D pie centimeters. Then we have a diagram with a clock face. All right. So what do we know? And what are we trying to find? Well, we do know that our radius of our circle from the center to the tip of the edge is equal to six centimeters. So our R is six centimeters, we know that the duration that this minute hand is moving around is all the way up to 50 minutes. So from 12 on the clock rotating clockwise, that's all the way over to where it's marked as 10, that's for 50 minutes. And we're trying to find the distance traveled around there. Or in other words, we're trying to find the arc length of a sector of a circle. And we recall from previous lessons, we've got a formula for that. That formula is S equals R theta. We've got R, that's great. We can plug in for R six centimeters. We just need to multiply that by theta. So what's our angle measurement going all the way around for minutes? Well, we know that we're going around an entire rotation would be for 60 minutes, but we're only going for 50 of that. So we're going for 50/ of rotation. And we're expressing our answer in terms of pi. So thinking about our angles in radiance, an entire rotation would be two pi so we can multiply 50/60 of a rotation by two pi an entire rotation and 50/60 of an entire rotation. When we multiply that out is equal to five pi divided by three. That's our theta. So we can plug that into our equation. We've got S equals for R that's six centimeters multiplied by theta, that's five pi divided by three. And then when we do that multiplication, it simplifies to B, all the numbers are 10 and we still have pi and we still have centimeters. So 10 pi centimeters is the distance that that minute hand travels in 50 minutes. We look at our answer choices and this matches with answer choice B well done. We'll catch you on the next one.

Distance Traveled by a Minute Hand Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand. Leave answers as multiples of π . 30 min

Key Concepts

Circumference of a Circle

Angular Motion

Arc Length

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