Let C = (3.15 m, 15 degrees above the neagtive x-axis) and D = (25.6, 30 degrees to the right of the negative y-axis). Find the x and y components of each vector.

Video transcript

Hey, everyone. So this problem is working with factors. Let's see what they're asking us. We have R one just given as 2.75 centimeters 28 degrees north of the negative X axis and R two which is 1.75 centimeters, 15 degrees west of the positive Y axis represent position vectors of two charged particles. We are asked to calculate the X and Y components of those two vectors. So the X and Y components mean that we are taking these vectors that are given to us in magnitude and direction and breaking them down into those X and Y components. So let's see, let's draw these vectors and see what they look like. So we have R one which is degrees north of the negative Y axis. So we've got the negative Y axis here. So yeah, R one, This angle is 28° and then we have R two which is 15 degrees west of the positive Y axis. So here's the positive Y axis, This will be R2 and that's 15°. So from here, we can see that the x component of our, of both R one and R two are going to be negative. And so we look at our multiple choice answers, I'm gonna read through those and we can start to deduce which ones just are not going to be correct. So a equals R1 x equals positive 2.43 centimeters, R one, Y equals positive 1.29 centimeters, R two, X equals positive 4.5 centimeters and R two, Y equals 1.69 centimeters. So because R one, X and R one, R two X are both positive and we know based off of drawing our graph and where these vectors are that, that is not correct. We can eliminate choice A B R one X equals positive 2.43 centimeters. R one Y equals negative 1.29 centimeters, R two, X equals positive 2.45 centimeters and R Y equals negative 1.69 centimeters. Again, R one X and R two X are positive. We know that that is not the case for our vectors. We can eliminate choice V choice C R one X equals negative 2.43 centimeters. R one Y equals positive 1.29 centimeters, R two, X equals negative 0.45 centimeters and R two Y equals positive 1.69 centimeters. OK. Here, both our R one X and R two X components are negative. Let's leave this choice here. D R one X equals negative 2. centimeters. R one, Y equals negative 1.29 centimeters, R two, X equals negative 40.45 centimeters and R two, Y equals positive 1.69 centimeters. Again, R one X and R two X are negative will leave that choice here. Let's look at our Y directions. Again, both of these components being that they are in the same quadrant, quadrant two have the same sign for their Y components. And they're both in the positive Y direction. And so from there, we can actually eliminate choice D so we are left with choice C as our only correct answer just based on the signs. But I'm going to walk through the map. So we can see how they got to these values just to make sure that we are on the right track. So we are going to use trigonometry. I'm gonna draw each of these vector in their magnitude and direction. And so this is our one And so this piece, this angle is 28°, right? This component is R one Y and then this is going to be R one X. So knowing that R one equals 2.75 cm which was given in the problem. And using our Sacla rules, R one x equals -2.75 Times the cosine of 28 which equals negative two point 43 centimeters. Again, we're, this is negative because we are in the negative X direction. Similarly, for R one Y we'll have the magnitude this time positive. It's on the positive Y direction 2.75 times the sign of 28 put that in and get 1.2, 9 cm. So we go back to for choice C and we can see that yes, R one, X negative 2.43 centimeters, R one Y positive 1.29 centimeters. So let's do the same thing for R two. So we have this triangle, this vector R two is equal to 1.7, 5 cm. And so this component here is gonna be R two X And then this here is R two Y were given The angle, there is 15° between our, the angle between the positive y axis and our vector. So again, using our SAA rules from trigonometry, we have R two, X Is equal to negative 1.75 Multiplied by the sign of 15 Which comes out to negative 0.4, five cm and RT Y Equals 1.7, 5 times the cosine of 15 Which comes out to 1.6, nine side papers go back up to choice C and we can see that yes, that is correct. R two X -0.45 cm and RTY positive 1.69cm. So choice C is the correct answer here. That's all we have for this one. We'll see you in the next video.