A spelunker is surveying a cave she follows a passage 130...

A spelunker is surveying a cave. She follows a passage 130 straight west, then 290 in a direction 45° east of south, and then 280 at 30° east of north. After a fourth unmeasured displacement, she finds herself back where she started. 1- What is the magnitude of the fourth displacement to two significant figures? 2- What is the direction of the fourth displacement?

Transcript

00:01 It is given that she started to walk towards west and covered the distance of 130 meters.

00:09 I am taking the positive x -axis as positive i -cap, negative as minus negative i -cap.

00:15 The same way, y, positive j -cap and minus y negative j -cap.

00:20 So if i consider s -1, this as s -1, so my s -1 vector will become minus 130 i of i -cap.

00:28 The same way, if this is s2, which is at 45 degrees east of south, this is east, west, north, and south, okay, this is east of south.

00:47 This is 45.

00:48 And again, she traveled towards 30 degrees east of north.

00:56 And then this is the unknown distance as she is back from where she started.

01:03 So if i start from s1, i get my s1 minus 130 icap.

01:08 This is s2.

01:09 I'm breaking this vector into components.

01:12 Y component will be 290 cos of 45 and x component will be 290 sine of 45.

01:22 So i will get my s2 vector as 290 cos 45 i cap minus 29.

01:34 2090 cos 45 j cap this will be 290 sign of 45 i cap x component okay so i will get this as 205 .03 i cap minus 205 .03 j cap as my result of s2 vector now this is s3 so i'm breaking this again into the components.

02:10 The x component will be 280 sign of 30 and the y component will be 280 cos of 30 degrees.

02:22 So my s3 vector will become 280 sign of 30 i cap plus 280 cause of 30 0 .48 jcap.

02:44 Now it is given that the curl is back from where she has started.

02:48 That means the total displacement is 0.

02:51 This is the starting point and this is the ending point as well...

Question

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