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(II) (a) At what upstream angle must the swimmer inProblem 67 aim, if she is to arrive at a point directly acrossthe stream? (b) How long will it take her?

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a) $56^{\circ}$b) $170 \mathrm{s}=2.8 \mathrm{min}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two or Three Dimensions; Vectors

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

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and our question, we're told. Ah, that eh? At what upstream angle must a swimmer and problem 67 Aim if she is to arrive at a point directly across the stream, and B, how long will it take her? So I wrote out here what we were given and were given that the velocity of the water relative to the bank. I write his visa w is equal to 0.50 meters per second. And the velocity of the swimmer, um relative to the bank is also 0.60 meters. There is 0.60 meters per second. Okay. And then I wrote up drew out the diagram here of what was in problems 67 years of the direction of the velocity of the water. You also have V s prime, which is the velocity of the swimmer relative to the bank. And I'll go ahead drawn the bank here is green sea of the bank on either side. Here is green. Okay. And then you also have the best, which is the actual velocity of the swimmer trying to swim from one direction to the other direction perpendicular to the bank. Okay, so we know the best. Prime No V f w And then for a It wants to know the angle Fada that we have here. Okay, well, we can use our trig metric identity that the sign of data sign is opposite overhype oddness. So sign of Fada is going to be equal to the opposite, which is the MW divided by the high partners, which is the best prime. Okay, And then to get data we want to solve for theta. So this is party. Actually, let's indicate that this is part of a oneself with data data is equal to the inverse sign which is signed in the minus one. A VW over V s prime. Lets go ahead, Right with D W is which is your 0.50 meters per second that's going be divided by B s prime, which is you're a 0.60 meters per second, the meters per second cancel so you don't have to write those. If you take the inverse sign of that ratio there you will get 56.44 degrees which Celt report to the correct number of sick. It significant digits is approximately 56 degrees. So that was your solution apart, eh? Now, Part B wants us to find how long it's going to take her to Transbourse from one bank to the other. Well, we're also I didn't write this down. Bullets go ahead. Indicated now the distance between the two banks. Let's call that D because equal to 55 meters. So we wanted to figure out the time it's going to take her to Tran verse this entire thing. Well, let's get a new page going here. This is part B. Distance is equal to the velocity times the time, and this velocity is going to be the velocity in, um VMs. This is going to be the SS. Okay, So at the time, which is what we're trying to find is going to be equal Tio d divided by the S. This is going to be equal to 55 meters, divided by via vests. Well, that's going to be the best prime times to co sign of the angle to be a less prime Times co sign of data. Okay, well, you know, the best prime is and found data. Last times. That's going to be 55 Meadors divided by the best prime, which is 0.60 meters per second Times co sign. And then the angle we found was about 56 degrees. But it was 56.4 for exactly your approximately 56 degrees. So we'll just write 56.44 degrees. No, in all of that is under that in the denominator. Okay, so if you plug all of this into our calculator, we find that this equals 170 seconds her and seven seconds, which in minutes is equal to 2.8 minutes because they're 60 seconds and every minutes he just divide that by 60 to get it in two minutes can box that in their solution party.

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