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Problem 29 Easy Difficulty

A river has a steady speed of 0.500 $\mathrm{m} / \mathrm{s}$ . A student swims upstream a distance of 1.00 $\mathrm{km}$ and swims back to the starting point. (a) If the student can swim at a speed of 1.20 $\mathrm{m} / \mathrm{s}$ in still water, how long does the trip take? (b) How much time is required in still water for the same length swim? (c) Intuitively, why does the swim take longer when there is a current?

Answer

(a) $t = 2016.8 \mathrm { s } = 33.61 \mathrm { min } = 0.56 \mathrm { h }$
(b) $t = 1666.67 \mathrm { s } = 27.78 \mathrm { min } = 0.46 \mathrm { h }$
(c) $v _ { \mathrm { av } \mathrm { F } _ { \mathrm { c } } } > v _ { \mathrm { av } \mathrm { k } _ { \mathrm { c } } }$

Discussion

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IN

Ibnu N.

November 10, 2020

Video Transcript

here we will consider The flow of water is in the positive Accid addiction s child seems first after dream. So the initial direction of child is in the negative exit direction and in downstream. The direction of child is in the positive exit direction. Yes, we are given Neville, Austria, of water. We respect to ground, which is zero point five meter parse Egan. We are also given the C Peter Boy we respect to steal water, which is 1.2 m Parseghian. Now we can write our relation for C Peter Boy. We respect to ground far upstream. That will be with this job. Boy, we respect the ground for upstream that is equal to rush job y respecto water minus last year off water respecto ground as so Peter boy, we respect toe attorneys 1.2 major part sicken. And so, Peter, water respect. Ground is 0.5 m Parsigian. This gives us last year of water. Sorry, sir Peter Boy, we respect ground for upstream. Equal toe 0.7 meter bar skin in downstream. It's a bit off water We respect to ground and see Peter Boy, we respect the water. Are in the same direction so we can write, Sir Peter Boy, we respect to ground for Don't stream equal toe, Sir Peter. Water Respect Ground plus, Sir Peter Boy, we respect water. It's a bitter water respect. Ground 0.5 m Parsigian. Andi So, Peter, off. Why we respect the water is 1.2 major part sicken. This gives us a Peter boy with respect to ground Far downstream equal toe one point seven meter parse again so related to ground See, Peter boy in downstream is greater than see Peter Boy in upstream is we are given the distance covered by boy in absolute dream trip is equal toe one kilometer which is equal to 1000 meter as a boy reaches back to its initial position So distance covered in absolute dream trip is equal Toe the sense card in down straight down city Um trip Now we can calculate time taken by boy to complete one trip So we have time Equal toe time Taken toe complete ab stream three plus time taken by boy to complete downstream downstream Chief as time taken to complete absolute dream trip is equal Toe descends in absolute dream trip which is 1000 m divided by see Peter Boy in upstream cliff which is 0.7 m par sicken plus the sense covered in downstream trip which is also equal 2000 m divided by see Peter Boy in Dome she dream tree we respect to ground is 1.7 m per skin. This gives us the total time taken by boy in the drift equal toe 20 16 wide air sicken By converting this time into minute, we will get time equal to 36 33.61 minute on this will be called Tau zero acquired 56 are I mean the next part off this problem. We want to find the time taken by the boy to complete one trip in Stillwater s video Already considered that the directional boy in upstream is in the negative exit direction on directional boy in downstream is in the positive access direction. Your water is still so we can write superior water. We respect to ground equal toe zero No far the motion in now for the emotional boy in negative exit direction, we can write See, Peter boy, we respect to ground for negative access equal to see Peter Boy. We respect the water. Mhm water minus. It's a bit off water. Respect to ground. So here, step it up. Why respect the water is 1.2 m part sicken and superior water. Respect to ground zero. This gives us Senator Boy, we respect ground in negative exploration is equal toe 1.2 m par skin. Similarly, in the positive exit addiction, we will also have the same Sip it. So this is a sequel toe See, Peter boy, with respect to ground in positive AXA direction Now we can calculate total time taken by the boy to complete one trip in Stillwater Does it equal toe time taken, my boy to complete the trip in negative exploration which is equal toe distance covered in negative exploration that is 1000 m divided by supporting negative extradition which is 1.2 m person plus the sense covered in positive X direction that is 1000 m divided by distance in positive. Sorry, Sir Peter Boy in positive accident him which is also 1.2 m par sicken. This gives us time taken by the boy to complete one Chief in Stillwater equal toe. 16 66 567 That is equal toe 27.79 minutes. This is us equal toe zero wide 46 are now in C part Will fast ical Glad every sip it off. Why? Wendy is gone. So we have a recipe Equal toe total distance covered by boy divided by total time taken. So total distance covered in absolute dream dream and don't trip downstream drip equal toe 2000 major divided by total time Taken in party of this problem is 2016 point Mexican. This gives us the recipe in part of this problem Equal toe zero white, 992 m parts chicken. Now we will calculate the recipe off boy, when water is still that is equal to descends covered by boy which is again 2000 m divided by time taken by boy When water is still is 1666 requires 67 which we have calculated in part We have this problem. This gives us a recipe it, in this case equal toe 1.2 meter parts again. Now, by comparing these two values, it is clear that it is clear that the recipe Tea Boy in Stillwater is greater than a recipe off. Bye. In in water. Wendy is gunned. Now we can say that the boy takes longer time Longer time when there is guns.

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