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IT TAKES YOU 10 MINS AND 30 SECS TO WALK AROUND ATRIANGULAR. THE PARK IS AN EQUILATERAL TRIANGLE WHOSE SIDE IS 0.50KM. YOU END UP EXACTLY THE SAME PLACE THAT YOUSTA...

Question

IT TAKES YOU 10 MINS AND 30 SECS TO WALK AROUND ATRIANGULAR. THE PARK IS AN EQUILATERAL TRIANGLE WHOSE SIDE IS 0.50KM. YOU END UP EXACTLY THE SAME PLACE THAT YOUSTARTED. A. WHAT IS YOUR DISPLACEMENT?B. WHAT WAS YOU DISTANCE TRAVELLED?C. WHAT WAS YOU AVERAGE VELOCITY?D. WHAT WAS YOU AVERAGE SPEED?

IT TAKES YOU 10 MINS AND 30 SECS TO WALK AROUND A TRIANGULAR. THE PARK IS AN EQUILATERAL TRIANGLE WHOSE SIDE IS 0.50 KM. YOU END UP EXACTLY THE SAME PLACE THAT YOU STARTED. A. WHAT IS YOUR DISPLACEMENT? B. WHAT WAS YOU DISTANCE TRAVELLED? C. WHAT WAS YOU AVERAGE VELOCITY? D. WHAT WAS YOU AVERAGE SPEED?



Answers

A person walks a distance of $3.0 \mathrm{km}$ due south and then a distance of $2.0 \mathrm{km}$ due east. If the walk lasts for $3.0 \mathrm{h}$ find (a) the average speed for the motion; (b) the average velocity.

This question covers the concept of the every speed and every speed is the total distance traveled upon the total time and the concept of the average velocity and the average velocity is the total displacement upon the total time. So we need to draw the coordinate system to solve our problems along the east. We consider the positive X. Axis along the north, we consider the positive Y axis. So the person traveled from origin towards the south and let's say it reached the point A. And that The changes cover this three km and from point A. To point B. It travels to us east and The length a B is two km. Okay, so for part A the total distance covered is oh A plus A B And that equals three kilometers plus two kilometers. Are the two traditions covered is five km, so that every speed Equals the total distance covered, that is five km upon the total time taken. That is three outs. Or the average speed equals 1.67 km. For our. Now, for part B, we need to calculate their displacement and the displacement equals the magnitude is square root off The displacement along south, that is three km square Plus the square of the displacement along the east. That is two km square. Or the displacement equals ah 3.61 kilometers. Okay. And the direction theater is uh, this single theater from south equals then it was off The displacement along east that is two km Upon the displacement long. South that is three km. Uh The angle theater equals 33.4°, So the average velocity equals the total displacement that is 3.61 km upon the total time, that is three hours are the vegetable city equals 1.2 km Power, and the direction is uh 33.4° east of South.

This question cover the concept of the displacement and the displacement is the final position. Minister initial position and the other concept is the concept of the average velocity and the average velocity is the displacement upon the time taken. So, first person worked towards the east and he works uh 230, meters. So from origin to east. And let's say this is point A. And the length is 1250 peters. And again he works towards south Up to 900 m, that's at this point b. And so the coordinate of the Point B will become 1-50 uh meters comma minus 900 meters. So the displacement of the person for part A, the displacement is the final operation. That is 1250 m. I had -900 m. Jihad minus the initial version, that is zero, I had plus zero jihad. So the displacement of the person is 1250 m. I had 900 m jihad. For part B. The average velocity Is the displacement upon the time and the displacement is went to 50 meter. I had -900 m jihad upon the time, And the time is 1220 minutes. That is 20 In 2/62. So the average velocity of the person is uh huh. 1.04 m/s. I had -0.75 meters pose again Jihad.

So we have this problem here, which involves a triangular park and some questions on it. Okay, so we have part A. We just find the distance around the park to the nearest yard. And so we see our park here has is basically a right triangle, and one side, this one that I have highlighted in red here is from 10 to eighties. That's about 70 yards long, and over here we have a side that's about from 10 2 50 50 I believe that's 40 yards long. And so now we have to find the distance of the iPod news. And that's that. Just 40 squared plus 70 squared. That's a squirt of that is going to the Oakland D is going to be equal to D. Let me just pull my calculator here and actually equal to 40 times. 40 is 1600. That's 4900 that's 6500 the square root of 6500 is about. It's called at 80.6. It's about 80.6 okay, so that's only this in the distance of D, and so the distance around the park is the distance of the other two summed with this distance. So I'll call the 80.6 plus 40 plus 70 40 plus 70 is 110 and 1 10 plus of 80.6 is 190.6. And so the distance around the park is about 190.6 yards. Okay, so let's roll back these changes here and now we have a party which is a new path and bridge are constructed from point Q to the midpoint M of PR. Find Q M to the nearest yard. So we have a midpoint and with pure um, that's about here. And we have to find this distance, right. But first we have to find find them. All right. Oh, actually, second here we have. That's right. This answer down so we don't forget it because we might need it later. That's about 191 yards. Okay, so let's move on. To beat, you had to find this distance here, which I'll name D again. And first we have to find em. But to find em, we need the Cartesian coordinates of P and R and the coordinates of P R 10. 10 comma income of 50. All right, so and for our would do the same thing. We have our exported as equals 80 and our white corn. It is equal to 10. Perfect. So now we have to find the So m is equal to the mean of 10 and 80 witches of 45. And, uh, why is equal to the mean of 50 and 10 which is 30. And so that's our M. You know, we have to find a distance from cute to M. And Q is just 10 comma 10. And so we have to find a distance from 10 comma 10 to 45 common 30. And so that's just 35 squared. Plus 20 squared. Screwed of that. And that's gonna be equal to our D. And that should be about 40 yards. That's about 40 yards. All right, this is also in your It's okay. So now see a man. Drugs from P D. Q to M. R. Two Q and back to pee at an average speed of 150 yards for minute. Okay, How many minutes does a take? Okay, so he starts at P, so I'm gonna drown blue now. So this is Pete. He starts frumpy and goes to que, um from Q. He goes to em from m T. R. This is the man's route from M R. Two Q and back to Pee Pee, and then it goes back here at 150 yards from it. So first of all, let's try to find the length of total length that he that he John through. So that's actually just from Peter. Cue from Pete Acute. Looks like we have soapy. Is that by Cordant 50 and queues at the y Coordinate. 10. That's 50 from 50. Attendance. 40. So we have 40 from P. D. Q. And then he goes from cute M and we already found from Cuba M which the this distance here, right from B, which is 40 yards. That's another four yards. He goes from M Are you okay? And from empty art should be just the distance 191 yards over to write because M is the midpoint so plus 191 over to I can simplify that to say, 90 was 45. Let's do 95 95 is a good approximation Um okay, so now we do from our two Q and from Arctic you we have our eyes on the export 80 and key was on the X coordinate 10. So from 80 to 10 that's 70 seven units and back to pee. So well, that's the same distance is 40 except in reverse. So for you and that's ourselves, that's the distance. The total distance he he jogs. That's 44 46 80 80 plus 40 is 1 2120 plus 70 isn't 1 90 and 1 90 plus 95 is 285. That's about the total distance in yards that key jobs and he jogs. So now we just d'oh! Now this is just a little ratio here that we do to find the speed that he's job for. So 150 yards in one minute equals 285 yards. And how many minutes will call that? How many minutes? X And we just do this little three's rule. And so we have 285 over 1 50 equals X right? And that should be how many minutes it takes him. And that is just about 1.5 minutes

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


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