the-explorer-took-60-mathrms-130-mathrms-and-70-mathrms-to-travel-the-30-mathrmm-2-mathrmo-sqrt2-mat

Question

The explorer took $60 \mathrm{s}, 130 \mathrm{s},$ and 70 $\mathrm{s}$ to travel the $30 \mathrm{m}, 2 \mathrm{o} \sqrt{2} \mathrm{m},$ and 140 $\mathrm{m}$ north distances, respectively. What is the average velocity of the explorer over the total distance traveled? 
(A) 0.50 $\mathrm{m} / \mathrm{s}$
(B) 33.3 $\mathrm{m} / \mathrm{min}$
(C) 0.76 $\mathrm{m} / \mathrm{s}$
(D) 100 $\mathrm{m} / \mathrm{min}$

Salamat Ali · Accepted Answer

original lost e. So a ritual lost to be here. Izzy called thio Displacement Displacement to do wait it by dime. So displacement here divided time all the time. The displacement we found earlier is 1 30 So 1 30 in the total time is 260 seconds. So, are you ready this week? It zero point father meter per second. So the answer is a

Salamat Ali · Answer

the displacement. Often Explorer can be found by from a diagram. Um, so initially. So we&#x27;re, um So the displacement will be from here to here. So this is our displacement. To find this, we we don&#x27;t know this part. So will find this part. And we don&#x27;t know this part&#x27;s toe minus. So you find this. We call it a telex. He&#x27;s a work. This place is dispensed with the ex direction, which is a 30. So from here to here, we have a 30. This will be 30 30 plus 20 times square. Root off too. Calls 45 course, 45 degrees. This is called the O. So in a presentable is 50. Where&#x27;s Dewie can be found by, um 20 square root off two signed. 45 signed 45 plus 1 40 So this gives us, um 1 20 Then our displacement. The less we call this is a delicious will be equal to screwed off. They&#x27;ll x square plus delta y square and substituting the values for Del X and a Y. This gives us ah, displacement off 1 30 Media. So are what is right. End off the problem. Thank you for watching

Lauren Madey · Answer

pour this problem, we will be finding the displacement, average speed and average velocity of our motorcyclists. You&#x27;re given three snapshots of his speed over time. And with those we can draw that miss factors and get our total laughter. Displacement Factor three has two components, one in the Y direction in one in the X direction. We have to add up everything in the Y axis in the X axis, also known as Theo. I had access in the J high access. When we do this, we get both the ladies of our little resulting triangle, which makes this fullness look a lot simpler. The idea courses are resulting vector, also known as the displacement vector. So for the first little leg of our resulting triangle, we have to add a vector one because it is in the Y axis and the y point of actor three because it is in the axis as well. We use this formula to find the displacement of Vector One and a Vector three spy component. You&#x27;re better threes. Why component? We have to take the displacement. She&#x27;s big are and terms it by signed 45 because it is in the Wycombe phone. Now this angle will change if you have a different angle. But we were given northwest which is 45 degrees. We have those together we get now you 2327 and the negative J had directional from the south for the second leg of our result in triangle we have to add a vector to placement and the X component of vector threes displacement. You do the same thing here with beckoned three taking the displacement in time to get by co side 45 could sign because portions of the X component we had those two up in the second leg of our results in triangle is negative. 4000 to hundreds of a three. Native indicates direction, by the way from vector so negative, just meaning that it is the negative X direction or the negative. I have direction. Then, for your resultant better or displacement vector, you basically just put them in like this to indicate the two components of your vector. The next part of this problem is finding the average speed. So you take your total distance over two time far into the distance tone distance. Think of total displacement You just take what we did last time. Multiply the velocity by the time add it all together to get the total say with the time and you get our average speed to be 23.3 meters per second. Final part of this problem Ask for the average velocity average philosophy being the magnitude of the displacement over total time. Now magnitude is basically the square root of the X components squared plus the wife of butter squared. So we take our ex components There are why converted square and stick them under a square root And then we calculate the total time this average velocity being 13 by five meters per second in the direction of the displacement vector.

Averell Hause · Answer

so here for part A, we consider a displacement. Delta Axe would be equaling 8.50 kilometers per hour, multiplied by 35.0 minutes. And then we&#x27;re multiplying this by one hour for every 60 minutes, and we have that the this would be plus 130 kilometres. So we have that the total displacement for the motorists would be equaling 180 kilometers. This would be our final answer for part A for part B. Then we want to find a total elapsed time. This would be dealt a tee total and this would be equaling 35.0 minutes plus 15.0 minutes. This would be multiplied by one hour for every 60 minutes plus 2.0 hours and we find that Delta T total is equaling 2.83 hours. So essentially her the motorists average velocity would be equaling Delta X over Delta T. So this would be equal in 180 kilometers divided by 2.83 hours and this is giving us 63.6 kilometers per hour. This would be our final average frontal answer for the average velocity for part B. That is the end of the solution. Thank you for watching

Averell Hause · Answer

so we can say that for part A, the magnitude of the displacement is gonna be equal. In the square root of 2.0 kilometers quantity squared plus 3.0 kilometers squared. This would be equaling 3.6. You could say 3.61 kilometers. This would be the magnitude of our displacement. Four part a. Now four part. Uh, we want to say that we also want to find the direction for the for the displacement, rather so we can say that fate as equaling are tan. And we&#x27;re travelling, uh, two kilometers north three kilometers east. So this should be the Ark 10 of 2.0 kilometers, divided by 3.0 kilometers two kilometers north three kilometers east. That puts us in the first quarter it so this is actually gonna be 33.7 degrees above the positive X axis. So this would be our answer for part a four part B. Then we want to find the average velocity. The average velocity is actually gonna be equaling the magnitude the displacement divided by time. And so this would be 3.61 or rather Let&#x27;s round at the very end. So 3.6055 kilometers divided by 2.50 hours. This is giving us 1.44 kilometers per hour. And again it&#x27;s the same exact direction, 33.7 degrees above the positive max access, or 33.7 degrees north of east. And then finally, for part C, we could say that what is her average speed world? Her average speed is actually going to be. There&#x27;s no direction. So her average speed is simply going to be equally the total distance traveled, which in this case is 2.0 kilometers plus 3.0 kilometers. And then this would be divided bye again, 2.50 hours. And so this advert speed which actually takes into account the path traveled, is equaling two kilometers per hour. This would be our average speed. That is the end of the solution. Thank you for watching

Henrique Saito · Answer

all right, so this question is about average velocity. And so we have this speedboat and it has to sort of legs. It&#x27;s traveling at two different speeds at two different directions, And so first we have to calculate the average speed. So for the first part of the trip, the boat is heading west in a straight horizontal line for 20 minutes, and it&#x27;s traveling at 108 kilometers per hour. And then the second part of the trip it&#x27;s there&#x27;s traveling at six degrees south of West. And so it&#x27;ll look something like this, right. If we have this vertical line, this is South, and this for the client will be west. So this is this is 60 degrees and we know that it&#x27;s traveling in 90 kilometers per hour and it&#x27;s going to be, and it&#x27;s gonna be having for 10 minutes. Okay, so what is the average speed? The average speed is pretty easy. Way to do it, sort of weighted average calculation. Where we have 108 Columbus per hour. Our average speed is 100 columns from our times 20 minutes. Okay. Plus the 90 kilometers per hour happening yet. 10 for 10 minutes. So we just divide this whole thing with a total time. She&#x27;s 30 minutes and we get our answer off, Uh, the average speed being 100 and two kilometers per hour. So that&#x27;s their answer for Bree, part B. You have to find the average velocity. Now, this is very, very still into the average speed part. Except we gotta split two since tax. And why components first. Okay, so if we take the second part and we split this into the excel like opponents kind of like this, uh, we can do some, You do some maths. And would you call this three degrees? How you do the other way around? It doesn&#x27;t really matter. Um, if we find that the why component of this boat velocity is going to be 77 0.9 kilometers per hour and the X component is going to be 45 Former spare, right? So this is just don using, you know, right angle sign and coast functions. You know, for example, to find 77.9. All you gotta do is you gotta multiple 90 Khost 30 Right, you evil, 77.9 Okay, so that&#x27;s cool. So let&#x27;s find the average velocity using the same method. We different speed for the X Opponent will do it for the white proponent, and then we&#x27;ll combine them too. Right, So we have average X velocity. It&#x27;s gonna be able to, uh it&#x27;s still just 108 times 20 minutes. But this time, instead of 90 clones per hour, it&#x27;s gonna be 45 kilometers an hour for the other 10 minutes. And so providing this by 30 the average X Solossa T is going to be, um, 87 kilometers per hour. Okay, And then we take the average y velocity, and that&#x27;s going to be just the 77.9 closed for our times of 10 minutes, divided by the 30 total minutes, and that&#x27;s going to be 26 kilometers per hour. So now we have this average velocity vector that is here, let me draw the sort of west and south think coordinates. So we have 87 kilometers per hour west and 26 south little kind of like this, right? We have the X and the Y components, and we here we have the exit point being He&#x27;s seven kilometers per hour, the wife of one of B 26 bombers per hour. So we have to find the magnitude, and we have to find the angle so the magnitude is just gonna be. But Tiger Steam 26 squared plus 87 squared square root of that is equal to, um, let me just do that really quickly. That&#x27;s gonna be about 90.8 Clemens per hour in terms of the angle. Well, we can just use the university arms kind of fix this up a bit. Ah, we can use the universe tan function to find the angle opposite being 2600 for hours adjacent 87. And we can just do this and calculate the angle, and that&#x27;s going to be 16 0.6 degrees. And so that would be, um, southwest. And there&#x27;s our answer. Here&#x27;s the magnitude of the average velocity and here&#x27;s the direction of the average velocity. And there you go

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Problem 3 Medium Difficulty

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