wait but isn't the arclength not the diameter itself though? wouldn't you have to set it to 2pi (because you found the arclength of the crater it would be 180 degrees) and then solve for r, and follow up with multiplying it by 2?

I have some arguments from trigonometry students and their teacher reasoning that for #24 (chapter 3) the answer would be 0. I know this text states on page 63 that Sin2theta is 1 but their reasoning being supported by the calculator is convincing. Would you be able to give more insight to this question?
Thank you.

Hi cmorales, thank you for your question. The textbook question asks "What is the maximum horizontal range of your gun?". The gun is able to shoot, since we're given data about how long a shot straight up takes to return to the gun. This data is useful to determine the initial velocity that's possible for the gun. With that initial velocity in mind, we can calculate the maximum possible range, and it will certainly be more than zero. The angle at which the range is maximum is $45^\circ$, and taking the sine of two times that gives "one", which is the greatest possible sine value of any angle. Keep in mind that we're maximizing horizontal range, not vertical height... I'm just guessing at where the misunderstanding might be...

My homework wanted to see the answer for part B in N*s. My homework is through Pearson Mastering Physics so, I'm not sure if this would apply to everyone.

Hi ragnarlaki, thanks for the comment. This is #13 in my copy of the 7th Edition. Are you using the "Global Edition", perhaps? Solutions for that are here: https://www.giancolianswers.com/giancoli-physics-7th-global-edition-chap.... If not, I'd be curious as to what the ISBN is for your copy of the textbook.

For part c, how can you be certain to use 233.33 m/s as your velocity if this is the velocity give by the problem for the lowest point of the loop? I solved the problem by using 6.0g as my radial acceleration (i got the correct answer but I'm not sure why). Thank You.

Hi maizer01, thanks for the question. Are you referring to the 1/2 in front of each kinetic energy term in part b)? They don't cancel since 1/2 is not a common factor of all terms. There is a potential energy term which is not multiplied by 1/2, which means 1/2 is not a common factor.
All the best,
Mr. Dychko

Hey, would you be able to put up the solution for question 13 of the chapter? It was a question on the number of electrons transferred after charge transfer.

There is a mistake in the video. Although the text is correct when talking about the permeability constant you say 4pi x 10^-4 as the text shows, the correct number is 4pi x 10^-7

For part a, I made the kinetic energy zero thinking that the initial state would be when he was stationary on top of the platform (with only gravitational potential energy). Why is it wrong to use this as my initial state? I do understand how you made your initial state as the moment the person jumps off the platform.

For the two values of m2 that you calculated from the quadratic equation, how do you know that m2 is the larger value and not the other value from the quadratic equation?

Hi chaegyunkang, the presumption here is zero initial velocity, after which a force is applied in order to provide some acceleration. Bobsleds start from rest and the athletes run beside it, pushing it along, before jumping inside (which they do at the 75 meter mark in this case). I suppose some familiarity with bobsledding is called for here, but nevertheless, if an initial speed isn't given in a question, chances are it must be zero. The force applied gives extra acceleration (beyond that provided by gravity), not initial velocity.

Hi chaegyunkang, it's always true that kinetic friction is less than static friction, all else being equal. In this question, however, it doesn't really matter what type of friction is mentioned, since we're not given the coefficient anyway. What matters is the deceleration the car, from which we calculate the coefficient. Be it a static or kinetic coefficient is not important. The important thing is that the type of friction on the incline is the same type of friction on the level surface so that we can be sure that whatever we calculated on the level surface will still apply on the incline.

How do we know that it is a frictionless ramp? Is it because the question does not give us the coefficient of friction so we assume that it is frictionless?

Hi chaegyunkang, thanks for the question. Since the question has a truck driving on the ramp, we assume there is only rolling friction, which we assume is negligibly small. There is no sliding, so there's no kinetic friction. While there is static friction, since we assume the brakes are not being applied (since the ramp is used when the brakes have failed), this means the tire is not applying a horizontal force due to static friction, and so the pavement is not in turn applying a Newton's 3rd law reaction force on the truck. In other words, static friction is not slowing down the truck. There is only rolling friction, which we can ignore.

Question #39 a ball is thrown straight up with a speed of 36 m/s. how long does it take to return to its starting point. Question is my teacher teaches out of 7th edition I have 6th edition but can not find this question in my book or on this website.It says on top of my page ch# 2 and page ref 2-7 but cant find it also how come you don't post question you just go to answers only . need to see question sometimes so I can find which edition it is in.

Hi EddieG, thanks for the question. I would love to post the questions, but I've avoided that since it would be a copyright issue with the publisher since I didn't create the questions. Perhaps you can ask your teacher to photocopy just the problems from their 7th Edition text for your reference?
All the best,
Mr. Dychko

Thank you for the question. Adding vectors using components is one of the methods for adding vectors. The component method, which is probably the most popular method to use, involves finding the sum of the component of each vector along an axis, and then taking the total as the component of the resultant along that axis. Vrx = V1x + V2x is just an algebraic way of saying that.

Hi hugokatich, thank you for the question. It's important to notice the minus sign in the expression there, which doesn't go away after squaring -65. Yes, -65 squared becomes positive, but the expression is for finding a leg of a right triangle, not for finding the hypotenuse, so the expression has a minus between the squared terms. $\sqrt{90^2-(-65)^2} = 62.2$.

hi why in the bottom equation can you just say that average velocity is the two terms summed and divided by two if average velocity was previously defined as displacement over time? This seems like the equation for speed

Hi umajacobshome, thanks for the question. Average velocity is indeed defined as displacement over time, as you say. There is a special case though when acceleration is constant, in that the average velocity in this case can also be calculated as the sum of the initial and final velocities divided by 2. Written as an equation, that is to say $v_{avg} = \dfrac{v_i + v_f}{2}$ in the special case when acceleration doesn't change.

Hi justin.sunny.bains, thanks for the questions. We're looking at a diffraction pattern here, and I would suggest referring to Figure 24-21 from the textbook to see the pattern of minima in the diffraction pattern. They occur at integer multiples of the wavelength. The twist in this question is that it tells us the position of the maxima, for which we need to deduce a formula from Figure 24.21. The maxima occur half way between the minima, so we need to add 1/2, as in $D \sin{\theta} = (m + \dfrac{1}{2})\lambda$.

Hi justin.sunny.bains, thanks for your question. I suppose the better answer would have a negative sign, but I didn't feel it was that important in this case. The negative sign is meant to indicate that the induced EMF creates an induced magnetic flux that opposes the change in magnetic flux in the solenoid. This means the induced EMF will have a direction opposite to the EMF that increased to the 5.0 A current. Outside of that, we don't really have a circuit diagram with a specific direction specified, so it's not really clear otherwise what direction a negative sign would mean. Nevertheless, given a choice between the two answers, including a negative would be a marginally better answer.

Hello cm2hn, have you tried this video again? In case the Javascript enabling the PDF embedded display was interfering with viewing the video, I have made the PDF into a clickable link instead. I havn't heard reports from other students about difficult viewing videos, so I suspect it's an isolated issue. Please try the video again and let me know if there are still any problems.

I think the answer to this question is wrong. The coordinate of the resultant vector is (-142.2 , 65) which means that it is located in quadrant 2. Since the value of tangent is negative in quadrant 2 it makes sense as well. The angle is 24.56 degrees above the negative x - axis, not positive x-axis.

Hi chaegyunkang, thank you for spotting that, and for the thoughtful analysis. You're quite right! I'll change the written answer, and made a note about the video.
All the best with your studies,
Mr. Dychko

If I am not familiar on the sine law and I am not being instructed in the sine/cosine law, what formulas from the book can be used to arrive at the same solutions?

So... the alternative to using the sine law here (or cosine law in other questions) is to do a lot of work resolving vectors into components, adding those components, then using the Pythagorean Theorem to turn the resultant components into the final resultant vector. The sine and cosine laws are designed to make the solution much, much quicker, and I'm quite sure the time you put into learning them will pay off by avoiding the much larger amount of time dealing with components. Places to start would be https://en.wikipedia.org/wiki/Law_of_sines and https://en.wikipedia.org/wiki/Law_of_cosines. Short term pain for long term gain!
Good luck,
Mr. Dychko

I'm confused on why the last problem did not utilize the Pythagorean theorem to find the actual speed traveled by the swimmer and the actual distance traveled, but for this problem, we did both... I solved the last problem (#46) using the a^2 + b^2 approach and found the angle using the inverse tangent, but my answer was wildly different. Any insight into how to reconcile this in my brain?

Hi brysongrondel, thanks for the question. I understand that something here is confusing, but it isn't clear to me which question/solution you're comparing with, since #46 isn't really comparable to this one... I notice you asked another question, so I'll follow up there.

So, first off, I have to say that I love this site so far. I am kind of struggling with the issues that arise from rounding errors. I am familiar with significant figures, but I am wondering if there is a better rule of thumb. Normally I don't round until I get the final answer, but I got problem #7 wrong. On this problem, I did all of the steps correctly, but I rounded up the times t1 and t2 to 2 sig figs and ended up getting 62 km/h. Is there anything I should know that might be helpful as I prepare for tests and future problem sets?
Thanks!

Hi brysongrondel, thank you very much for the nice feedback, and your question. The general idea is to avoid rounding until the final answer. Rounding values before a final answer is called intermediate rounding error, and causes the final answer to differ as a result of the rounding. So, generally, avoid rounding until the end. It's a topic that calls for a bit of patience since most numbers need rounding eventually, and the answer you're comparing to may have chosen a different number of digits than you, resulting in a different answer than what you obtained despite your following the best practice of keeping "lots" of digits until the end. Different people could have different opinions on what "lots" means. I would say that two additional digits, beyond those that are significant , should be kept with intermediate numbers.
Hope that helps,
Mr. Dychko

## Giancoli 7th Edition, Chapter 8, Problem 3

By maizer01 on Sun, 11/11/2018 - 07:27wait but isn't the arclength not the diameter itself though? wouldn't you have to set it to 2pi (because you found the arclength of the crater it would be 180 degrees) and then solve for r, and follow up with multiplying it by 2?

## Giancoli 7th Edition, Chapter 3, Problem 24

By cmorales on Thu, 11/01/2018 - 14:22I have some arguments from trigonometry students and their teacher reasoning that for #24 (chapter 3) the answer would be 0. I know this text states on page 63 that Sin2theta is 1 but their reasoning being supported by the calculator is convincing. Would you be able to give more insight to this question?

Thank you.

Hi cmorales, thank you for your question. The textbook question asks "What is the maximum horizontal range of your gun?". The gun is able to shoot, since we're given data about how long a shot straight up takes to return to the gun. This data is useful to determine the initial velocity that's possible for the gun. With that initial velocity in mind, we can calculate the maximum possible range, and it will certainly be more than zero. The angle at which the range is maximum is $45^\circ$, and taking the sine of two times that gives "one", which is the greatest possible sine value of any angle. Keep in mind that we're maximizing horizontal range, not vertical height... I'm just guessing at where the misunderstanding might be...

## Giancoli 7th Edition, Chapter 26, Problem 26

By ZreLL on Thu, 11/01/2018 - 13:29My homework wanted to see the answer for part B in N*s. My homework is through Pearson Mastering Physics so, I'm not sure if this would apply to everyone.

## Giancoli 7th Edition, Chapter 16, Problem 13

By ragnarlaki on Fri, 10/19/2018 - 06:58Oh I’m sorry, I didn’t realize I had the global edition

No worries, and thanks for letting me know that solved the problem!

## Giancoli 7th Edition, Chapter 16, Problem 13

By ragnarlaki on Thu, 10/18/2018 - 09:18This is not problem 13, 7th edition

Hi ragnarlaki, thanks for the comment. This is #13 in my copy of the 7th Edition. Are you using the "Global Edition", perhaps? Solutions for that are here: https://www.giancolianswers.com/giancoli-physics-7th-global-edition-chap.... If not, I'd be curious as to what the ISBN is for your copy of the textbook.

Best wishes,

Mr. Dychko

## Giancoli 7th Edition, Chapter 5, Problem 12

By chaegyunkang on Wed, 10/17/2018 - 17:00For part c, how can you be certain to use 233.33 m/s as your velocity if this is the velocity give by the problem for the lowest point of the loop? I solved the problem by using 6.0g as my radial acceleration (i got the correct answer but I'm not sure why). Thank You.

Oops I misread the part where it said "same speed".

## Giancoli 7th Edition, Chapter 6, Problem 36

By maizer01 on Sun, 10/14/2018 - 16:23what about the 1/2's? don't they cancel?

Hi maizer01, thanks for the question. Are you referring to the 1/2 in front of each kinetic energy term in part b)? They don't cancel since 1/2 is not a common factor of

allterms. There is a potential energy term which is not multiplied by 1/2, which means 1/2 is not acommonfactor.All the best,

Mr. Dychko

## Giancoli 7th Edition, Chapter 7, Problem 28

By kim.c13 on Wed, 10/10/2018 - 23:19On this problem, the equation for elastic collisions is vA - vB = v'A - v'B, but why is the one on #25 negative for the final velocity (v') side?

Wait! Nevermind - got it.

## Giancoli 7th "Global" Edition, Chapter 16, Problem 10

By hugokatich on Thu, 10/04/2018 - 23:24Hey, would you be able to put up the solution for question 13 of the chapter? It was a question on the number of electrons transferred after charge transfer.

Hi hugokatich, isn't question 13 here: https://www.giancolianswers.com/giancoli-physics-7th-global-edition-solu...?

## Giancoli 7th "Global" Edition, Chapter 18, Problem 33

By ingimar2112 on Thu, 10/04/2018 - 13:20nice

Thanks!

## Giancoli 7th Edition, Chapter 20, Problem 26

By ZreLL on Sun, 09/30/2018 - 09:17There is a mistake in the video. Although the text is correct when talking about the permeability constant you say 4pi x 10^-4 as the text shows, the correct number is 4pi x 10^-7

Thank you very much ZreLL, I've added a note to the quick answer mentioning this error.

All the best,

Mr. Dychko

Your welcome. Thank you for all the help with physics.

## Giancoli 7th Edition, Chapter 6, Problem 38

By chaegyunkang on Sat, 09/22/2018 - 07:03For part a, I made the kinetic energy zero thinking that the initial state would be when he was stationary on top of the platform (with only gravitational potential energy). Why is it wrong to use this as my initial state? I do understand how you made your initial state as the moment the person jumps off the platform.

## Giancoli 7th Edition, Chapter 5, Problem 31

By chaegyunkang on Tue, 09/18/2018 - 16:35For the two values of m2 that you calculated from the quadratic equation, how do you know that m2 is the larger value and not the other value from the quadratic equation?

## Giancoli 7th Edition, Chapter 11, Problem 21

By kevin.rosario on Sat, 09/15/2018 - 23:12I did part A on my calculator and I came up with 22.64942355. How did you come up with 2.29Hz?

Thank you.

## Giancoli 7th Edition, Chapter 4, Problem 63

By chaegyunkang on Sat, 09/15/2018 - 16:18How do we know that the initial velocity is zero? If it was given a push I thought it would be a non-zero velocity.

Hi chaegyunkang, the presumption here is zero initial velocity, after which a force is applied in order to provide some acceleration. Bobsleds start from rest and the athletes run beside it, pushing it along, before jumping inside (which they do at the 75 meter mark in this case). I suppose some familiarity with bobsledding is called for here, but nevertheless, if an initial speed isn't given in a question, chances are it must be zero. The force applied gives extra acceleration (beyond that provided by gravity), not initial velocity.

Best wishes with your studies,

Mr. Dychko

## Giancoli 7th Edition, Chapter 4, Problem 61

By chaegyunkang on Sat, 09/15/2018 - 16:03If the car was skidding what difference would it make to the problem? Does it change to kinetic friction when it starts to skid?

Hi chaegyunkang, it's always true that kinetic friction is less than static friction, all else being equal. In this question, however, it doesn't really matter what type of friction is mentioned, since we're not given the coefficient anyway. What matters is the deceleration the car, from which we calculate the coefficient. Be it a static or kinetic coefficient is not important. The important thing is that the type of friction on the incline is the

same typeof friction on the level surface so that we can be sure that whatever we calculated on the level surface will still apply on the incline.All the best,

Mr. Dychko

## Giancoli 7th Edition, Chapter 4, Problem 55

By chaegyunkang on Sat, 09/15/2018 - 14:39How do we know that it is a frictionless ramp? Is it because the question does not give us the coefficient of friction so we assume that it is frictionless?

Hi chaegyunkang, thanks for the question. Since the question has a truck driving on the ramp, we assume there is only rolling friction, which we assume is negligibly small. There is no sliding, so there's no kinetic friction. While there is static friction, since we assume the brakes are not being applied (since the ramp is used when the brakes have failed), this means the tire is not applying a horizontal force due to static friction, and so the pavement is not in turn applying a Newton's 3rd law reaction force on the truck. In other words, static friction is not slowing down the truck. There is only rolling friction, which we can ignore.

Hope this helps,

Mr. Dychko

## Giancoli 7th Edition, Chapter 2, Problem 42

By EddieG on Wed, 09/05/2018 - 18:50Question #39 a ball is thrown straight up with a speed of 36 m/s. how long does it take to return to its starting point. Question is my teacher teaches out of 7th edition I have 6th edition but can not find this question in my book or on this website.It says on top of my page ch# 2 and page ref 2-7 but cant find it also how come you don't post question you just go to answers only . need to see question sometimes so I can find which edition it is in.

Hi EddieG, thanks for the question. I would love to post the questions, but I've avoided that since it would be a copyright issue with the publisher since I didn't create the questions. Perhaps you can ask your teacher to photocopy just the problems from their 7th Edition text for your reference?

All the best,

Mr. Dychko

## Giancoli 6th Edition, Chapter 19, Problem 32

By thesouthportschool on Mon, 08/27/2018 - 18:10this is epic

## Giancoli 7th "Global" Edition, Chapter 3, Problem 16

By hugokatich on Mon, 08/20/2018 - 19:43Also, what rule did you use for the triangle in part b? Which rule indicates that Vrx = V1x + V2x?

Thank you for the question. Adding vectors using components is one of the methods for adding vectors. The component method, which is probably the most popular method to use, involves finding the sum of the component of each vector along an axis, and then taking the total as the component of the resultant along that axis. Vrx = V1x + V2x is just an algebraic way of saying that.

All the best,

Mr. Dychko

## Giancoli 7th "Global" Edition, Chapter 3, Problem 16

By hugokatich on Mon, 08/20/2018 - 19:39Where did the answer of 62.2 units come from? Given that the square root of 90^2 - (-65^2) is equal to 111.02?

Hi hugokatich, thank you for the question. It's important to notice the minus sign in the expression there, which doesn't go away after squaring -65. Yes, -65 squared becomes positive, but the expression is for finding a leg of a right triangle, not for finding the hypotenuse, so the expression has a minus between the squared terms. $\sqrt{90^2-(-65)^2} = 62.2$.

Best wishes,

Mr. Dychko

## Giancoli 7th Edition, Chapter 2, Problem 23

By umajacobshome on Thu, 08/02/2018 - 20:28hi why in the bottom equation can you just say that average velocity is the two terms summed and divided by two if average velocity was previously defined as displacement over time? This seems like the equation for speed

Hi umajacobshome, thanks for the question. Average velocity is indeed defined as displacement over time, as you say. There is a special case though when acceleration is constant, in that the average velocity in this case can also be calculated as the sum of the initial and final velocities divided by 2. Written as an equation, that is to say $v_{avg} = \dfrac{v_i + v_f}{2}$ in the special case when acceleration doesn't change.

Hope this helps,

Mr. Dychko

## Giancoli 7th Edition, Chapter 24, Problem 29

By justin.sunny.bains on Mon, 07/30/2018 - 16:06Why is m 1.5 and not just 1?

Hi justin.sunny.bains, thanks for the questions. We're looking at a diffraction pattern here, and I would suggest referring to Figure 24-21 from the textbook to see the pattern of minima in the diffraction pattern. They occur at integer multiples of the wavelength. The twist in this question is that it tells us the position of the

maxima, for which we need to deduce a formula from Figure 24.21. The maxima occur half way between the minima, so we need to add 1/2, as in $D \sin{\theta} = (m + \dfrac{1}{2})\lambda$.Best wishes with your studies,

Mr. Dychko

## Giancoli 7th Edition, Chapter 21, Problem 12

By justin.sunny.bains on Tue, 07/24/2018 - 17:23Should the answer be negative?

Hi justin.sunny.bains, thanks for your question. I suppose the better answer would have a negative sign, but I didn't feel it was that important in this case. The negative sign is meant to indicate that the induced EMF creates an induced magnetic flux that opposes the change in magnetic flux in the solenoid. This means the induced EMF will have a direction opposite to the EMF that increased to the 5.0 A current. Outside of that, we don't really have a circuit diagram with a specific direction specified, so it's not really clear otherwise what direction a negative sign would mean. Nevertheless, given a choice between the two answers, including a negative would be a marginally better answer.

Best wishes with your studies,

Mr. Dychko

## Giancoli 7th Edition, Chapter 4, Problem 22

By chaegyunkang on Sun, 07/01/2018 - 15:55where is the normal force for part a) ?

Oh, I realized that free body diagram only shows the forces acting on the object, not on other objects....

Yep, you got it! :)

## Giancoli 7th Edition, Chapter 19, Problem 20

By cm2hn on Sat, 06/30/2018 - 21:13Hello, I was trying yo watch the video, but it is unable to play. Thanks.

Hello cm2hn, have you tried this video again? In case the Javascript enabling the PDF embedded display was interfering with viewing the video, I have made the PDF into a clickable link instead. I havn't heard reports from other students about difficult viewing videos, so I suspect it's an isolated issue. Please try the video again and let me know if there are still any problems.

All the best,

Mr. Dychko

## Giancoli 7th Edition, Chapter 3, Problem 16

By chaegyunkang on Wed, 06/27/2018 - 20:21I think the answer to this question is wrong. The coordinate of the resultant vector is (-142.2 , 65) which means that it is located in quadrant 2. Since the value of tangent is negative in quadrant 2 it makes sense as well. The angle is 24.56 degrees above the negative x - axis, not positive x-axis.

Hi chaegyunkang, thank you for spotting that, and for the thoughtful analysis. You're quite right! I'll change the written answer, and made a note about the video.

All the best with your studies,

Mr. Dychko

## Giancoli 7th Edition, Chapter 3, Problem 48

By brysongrondel on Sat, 06/02/2018 - 20:49If I am not familiar on the sine law and I am not being instructed in the sine/cosine law, what formulas from the book can be used to arrive at the same solutions?

So... the alternative to using the sine law here (or cosine law in other questions) is to do a lot of work resolving vectors into components, adding those components, then using the Pythagorean Theorem to turn the resultant components into the final resultant vector. The sine and cosine laws are designed to make the solution much, much quicker, and I'm quite sure the time you put into learning them will pay off by avoiding the much larger amount of time dealing with components. Places to start would be https://en.wikipedia.org/wiki/Law_of_sines and https://en.wikipedia.org/wiki/Law_of_cosines. Short term pain for long term gain!

Good luck,

Mr. Dychko

## Giancoli 7th Edition, Chapter 3, Problem 47

By brysongrondel on Sat, 06/02/2018 - 19:58I'm confused on why the last problem did not utilize the Pythagorean theorem to find the actual speed traveled by the swimmer and the actual distance traveled, but for this problem, we did both... I solved the last problem (#46) using the a^2 + b^2 approach and found the angle using the inverse tangent, but my answer was wildly different. Any insight into how to reconcile this in my brain?

Hi brysongrondel, thanks for the question. I understand that something here is confusing, but it isn't clear to me which question/solution you're comparing with, since #46 isn't really comparable to this one... I notice you asked another question, so I'll follow up there.

## Giancoli 7th Edition, Chapter 2, Problem 12

By brysongrondel on Mon, 05/28/2018 - 16:30So, first off, I have to say that I love this site so far. I am kind of struggling with the issues that arise from rounding errors. I am familiar with significant figures, but I am wondering if there is a better rule of thumb. Normally I don't round until I get the final answer, but I got problem #7 wrong. On this problem, I did all of the steps correctly, but I rounded up the times t1 and t2 to 2 sig figs and ended up getting 62 km/h. Is there anything I should know that might be helpful as I prepare for tests and future problem sets?

Thanks!

Hi brysongrondel, thank you very much for the nice feedback, and your question. The general idea is to avoid rounding until the final answer. Rounding values before a final answer is called

intermediate rounding error, and causes the final answer to differ as a result of the rounding. So, generally, avoid rounding until the end. It's a topic that calls for a bit of patience since most numbers need rounding eventually, and the answer you're comparing to may have chosen a different number of digits than you, resulting in a different answer than what you obtained despite your following the best practice of keeping "lots" of digits until the end. Different people could have different opinions on what "lots" means. I would say thattwo additional digits, beyond those that are significant, should be kept with intermediate numbers.Hope that helps,

Mr. Dychko