Question

Suppose you walk 10.5 m in a direction exactly 16° south of west, then you walk 22 m in a direction exactly 42° west of north. Part (a) How far are you from your starting point, in meters? Part (b) What is the angle of the compass direction of a line connecting your starting point to your final position measured north of west in degrees?

          Suppose you walk 10.5 m in a direction exactly 16° south of west, then you walk 22 m in a direction exactly 42° west of north. 

Part (a) How far are you from your starting point, in meters? 

Part (b) What is the angle of the compass direction of a line connecting your starting point to your final position measured north of west in degrees?
        
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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Suppose you walk 10.5 m in a direction exactly 16° south of west, then you walk 22 m in a direction exactly 42° west of north. Part (a) How far are you from your starting point, in meters? Part (b) What is the angle of the compass direction of a line connecting your starting point to your final position measured north of west in degrees?
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Transcript

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00:01 In this video, we are going to find out the distance between starting point and the, we can say final point based on the given information.
00:07 So there is a person who is traveling in a certain direction at a certain angle.
00:12 So we can just denote or we can show how he or she is traveling based on the given information.
00:17 So this very angle is given in our problem as 16 degrees.
00:21 And this very length is 10 .5.
00:25 And now here we can say that this very angle will be here.
00:30 42 degrees and then here it can be written that this is our d2 vector and this one is our d1 vector.
00:38 So its length is 22.
00:40 Now here we can write that d1 vector will be equal to 10 point minus cost and then here we have 16 degrees i cap minus sine 16 j cap and now we can say that the value of this d1 vector can be written as.
01:00 Negative 10 .09 i cap and then here it is minus 2 .89 j cap and now we can say that the value of d2 vector will be equals to here 22 times cost 42 and then here it is i cap now it will be here minus sine 42 and then here it is j cap so from this very information we can say that d2 vector will be here equals to basically 16 .35 and then it is here i cap and then it will be minus 1 .72 j cap.
01:36 So from this very information it can be written that net displacement that is dr vector is equals to d1 vector plus d2 vector.
01:45 So this value will come out to be equals to here negative 24 .81 icap plus it will be here 13 .46 j cap.
01:57 So from this very information we can say that the value of magnitude of dr vector will be here equals to it will roughly come around 28 point it will be here to three.
02:10 So we have got the value or we can say answer for the first part of this very problem...
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