You are sitting at an outdoor cafe minding your own business...

You are sitting at an outdoor café, minding your own business, when a mischievous squirrel steals your croissant. The squirrel then runs away with your croissant in the following fashion: The squirrel runs North for 12m Then, the squirrel turns and runs East for 17m If you were to draw a straight line to the squirrel at this point, what angle would that line make relative to the positive X-axis (which is East on the compass)? The squirrel then runs up to the top of a tree, which is 15m tall. What is the exact straight-line distance now between you and the squirrel (and, more importantly, your croissant)? You are sitting at an outdoor cafe, minding your own business, when a mischievous squirrel steals your croissant. The squirrel then runs away with your croissant in the following fashion: 1.The squirrel runs North for 12m 2.Then,the squirrel turns and runs East for 17m If you were to draw a straight line to the squirrel at this point, what angle would that line make relative to the positive X-axis (which is East on the compass)? The squirrel then runs up to the top of a tree, which is 15m tall. What is the exact straight-line distance now between you and the squirrel (and, more importantly,your croissant)?

Transcript

00:01 Okay, so for the first question, we have to add the two vectors and draw the result done.

00:09 So in order to determine the angle that the vector with a 27 meters magnitude makes with the horizontal, so this angle, we will do this first.

00:25 Let's draw a vertical line here.

00:29 If this is 20 degrees, this is 90 degrees, then this angle is 70 degrees.

00:40 To complete 180 for a triangle then this 70 we have 50 here then this angle is 60 degrees so to complete 180 70 plus 50 plus 60 then if this is 60 then this one is 30 degrees to complete 90 degrees and then we can see that this is 20 degrees to complete 90 as well so 70 20 now that we know the angle that the vector with 27 magnitude makes with the horizontal we can solve this problem.

01:18 So to add two vectors we will add its horizontal and vertical components individually.

01:24 So for the horizontal component first we have 17 meters cosine 20 degrees.

01:32 Note that we use cosine here since the horizontal component is the adjacent side of the angle plus negative 27 meters cosine 30 degrees.

01:43 Note that this is negative since this vector points towards the negative x -axis if we follow the cartesian coordinate system.

01:51 So this is equals to negative 7 .4 meters.

01:55 Now for the vertical component, then we have 17 meters sine 20 degrees plus 27 meters sign 30 degrees.

02:06 Note that they are both positive since they points toward the positive y -axis.

02:11 That is for the vertical components, we have.

02:14 19 .3 meters.

02:17 Then the magnitude is the square root of the sum of the squared of its horizontal and vertical components.

02:25 So negative 7 .4 meters quantity squared plus 19 .3 meters quantity squared and this is equals to 20 .67.

02:48 And for the direction, we have tangent inverse of the vertical component over the horizontal so we have tangent inverse of 19 .3 meters over 7 .4 meters and the answer is 69 degrees and since the horizontal component is negative by the vertical component is positive it is on the quadrant 2 we have this so this is 20 .67 meters well, this is angle 69 degrees.

03:47 Now, the next problem, if you travel 25 meters is, and 48 meters south, what is the total displacement? that displacement, by definition, is the difference of the final and the initial position.

04:14 As such, from this point to this point, the length of that.

04:21 This is the displacement.

04:27 Then since it resembles a right triangle then the displacement is equals to the square root of 25 meters plus 48 meters square so being can find that displacement is equals to so the displacement is the sum of the squared of 25 and 48 if you follow the pythagorean current then this is equals to 554 .12 meters next we have here here, how far was the hole from his original position in what direction? so this distance to this distance.

05:20 If this is 10 meters southwest, then 3 meters north, then 4 meters south -east, and 0 .5 meters west...

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