Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

If a vector $\vec{A}$ has the following components, use trigonometry to find its magnitude and the counterclockwise angle it makes with the $+x$ axis: (a) $A_{x}=8.0$ lb, $A_{y}=6.0$ lb (b) $A_{x}=-24 \frac{m}{s}, A_{y}=-31 \frac{m}{s}$ (c) $A_{x}=-1500$ km, $A_{y}=2000$ km (d) $A_{x}=71.3$ N, $A_{y}=-54.7$ N

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

see solution

05:28

Bruce Edelman

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

University of Michigan - Ann Arbor

University of Washington

Hope College

McMaster University

Lectures

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

09:56

In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

05:33

$\cdot$ In each of the cas…

07:21

In each of the cases that …

10:41

03:26

Find the magnitude and dir…

03:03

Use a scale drawing to fin…

09:16

05:41

07:18

In each case, the $x$ - an…

06:57

In each of these, the $x$ …

05:40

What is the sum of the fol…

01:17

Find the $x$ and $y$ compo…

03:53

01:35

A vector $\vec{A}$ has com…

in this question. Um, we are given the x and Y components of Vector A. Okay, so, uh, you can write better in a X I had plus a y jihad. Okay, so to find a 22 of a okay, we'll be using, uh, Pythagoras theorem. Uh, x squared as a y square square roots. Okay. And then, if you want to find the angle, Okay, uh, in this case, we want to find a counterclockwise angle, uh, make with the positive X axis. So, in general, the angle can be found using tangent, uh, y devised by a ex. Okay, But since our if you draw the axis, the x and Y okay, you can see that there are four quadrants. Okay, in general, if you substitute a positive a y positive A X. This is the angle that you get. Okay, in some cases, uh, the vectors may draw into the second squadron like this or the squadron. Fourth quarter. Okay, But, ah, if you substitute the positive, uh, y divided by X or just, um, any two of em I devised by a ex, you're always going to get this, uh, acute angle. Mm. So there is with the horizontal axis. And then we're just a just, um, just to that it's just a calculation to find a counterclockwise anger with the positive X axis. Okay, so in this question, there are four parts were given for different components, set of components. So you find the magnitude and the direction, uh, the anger that makes with the positive X axis. Okay, so in part, they were given that a X is 8.0 power A y is £6.0 a and then, uh, 92 of a e x square plus in my square skyrockets. Yeah, it's square past six square square roots and you get a hand pump. Okay. And if you draw this, uh, dr Out, Okay, so it will be It looks something like this. So this is the angle that we are looking for. So this anger is a tangent. Um, n y u by by a x Okay. Uh, Hendren tree 6/8, which is three or four. Okay. And you get 36.9 degrees. Okay. Okay. Then be Maybe I'll give it a x s. My nurse. 24 years the second the y is minus 31. He does the second. So if you draw the rector Ah, it is in the third quadrant. That looks like this. Okay. And then the money to a Okay, um, a X square plus a white square route. He got 24 square plus 31 square and square root. This is the the 9.2 m per second and ah, uh, angle here. Okay. The data will be tangent. Um, a Why do I buy a X? Okay, you get the the one divided by 24 to calculate this. Ah, you get 52 52 degrees. He and then the anger. Arista. Positive acts access. Yes. 180 has apparently degrees plus 52 degrees. And get, uh, 232 degrees. Okay, so the answers for part B, 39.2 m per 2nd, 232 degrees. Okay, then. Posse. Um, we are given a x s negative 1500 km. The y yes, 2000 km. And so if he joined up, Okay, this is in the second quarter in, uh, looks like this. Why? He thinks this is our A, You know, I'm going to find this angle of data. Okay, so, um, the 22 e s a x square, plus a white square, I think the square root. So 1500 square plus 2000 square. It's where we're it. Take. You find 200 to 2500 camp. Yeah. Then, uh, the anger. Yes. Um, was it is X axis. They will be 180 degrees minus Attention. Okay, uh, one b y. Divided by X. Yeah. So you get, uh, around 27 degrees in this case, so the answer's, uh, 2500 km. 127 degrees. Daniel protein. Okay. Just to mention that this is, uh, data. Yeah. Yeah, but the whole thing. Yeah. And then, uh, body, we are given a excess 71.3 Newtons A y Yes, negative. 54.7 inch things. So if you draw it out, okay, it would be in the fourth quadrant. Okay? It looks something like this. Okay. And then you need this and potato later. Okay. So, the money to a yes x square, plus a white square square root. Calculate the as you get, um, 89.9 Okay, then the angle with positive X axis. He saw the anger. Is this big gang girl? So we try and 60 degrees minus data. Keep trying. 60 degrees minus attention. Uh huh. More A y do I buy a X? Yeah. And, uh, you substitute the numbers and you get 223 degrees. Okay. So, party, these are the answers, and that's all for this question.

View More Answers From This Book

Find Another Textbook