For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of (a) the vector sum A + B

Video transcript

Welcome back everybody. So we are asked to find the vector edition of C plus D. So let's go ahead and perform that addition here. Starting at the end of C. I'm going to add the vector D to it. We're gonna get something kind of like that. And just as a reminder, I'm going to mark this as our vector D. Now we are going to use the tip to tail method in order to find our resultant summed up vector. So starting at the origin and going to the end of our D vector that is going to be equivalent to C plus D. And I'm actually going to label this vector are now we are told to find the magnitude and direction of our so we are going to need some important formulas here. The magnitude of a given vector, let's say in this example vector A is going to be the square root of its x component squared plus its y component squared. And the direction of the vector is going to be the arc tangent of its y component divided by its x component. Well, what are the X and Y components of our Well, the X component is simply going to be the summation of the X components of our two vectors. So C X plus D. X. Same thing with our y component that is just going to be C, Y plus dy let's go ahead and find our X and our Y. So our X is equal to. Well, let's find c X here. See x is going to be this guy right here. So we're gonna have the magnitude of C. Times the co sign of our angle and it is going to be negative since we are going in the negative extra action plus D. X. So now we are looking at this guy, we have the magnitude of D. Times the sign of our angle and he is going to be negative as well because he is in the negative X. Direction. Plugging this into our calculator, we get negative 19.84 m. Great. So now let's do the same thing to find. Ry. Ry is C. Y. So we are now looking at this guy right here and that is going to be still the magnitude, see But now it's going to be times the sine of our angle and it is going to be negative since we are going in the negative Y direction plus our Dy so looking at this guy right here now, it's going to be the magnitude of D. Times the co sign of our angle and it's going to be positive since we're headed in the positive Y direction Plugging this into our calculator, we get negative 2.19 m. Now that we have our X. And our Y. Let's go ahead and find the magnitude and direction of our our vector. So the magnitude is going to be the square root of negative 19.84 squared plus negative 2.19 squared. And this is going to be equal to 19. m. Great. So now let's go ahead and find the direction of our our so we have the arc tangent of our Y component negative 2.19 divided by R. X. Components 19.96. This is going to be equal to 6.30°. But is this the angle that we're looking for? The angle that we actually found is this little sliver right here. But it is common practice to actually mark the angle counterclockwise from the positive X. Direction. So we are actually going to add 180° to this to get our final answer of 186.30°. So now we have found the magnitude of our r. And the direction of our r vector. Giving us a final answer of answer choice. A thank you guys so much for watching. Hope this video helped. We will see you all in the next one.