vectors

1. I Converting Velocity Vector Formula from Cartesian Coordinate System to Polar Coordinate System

I have a little question about converting Velocity formula that is derived as, $\vec{V}=\frac{d\vec{r}}{dt}=\frac{dx}{dt}\hat{x}+\frac{dy}{dt}\hat{y}+\frac{dz}{dt}\hat{z}$ in Cartesian Coordinate Systems $(x, y, z)$. I want to convert this into Polar Coordinate System $(r, \theta)$...
2. I Div Grad Curl question

I'm reading div grad curl for my math methods class, and I came across this question: "Using arrows of the proper magnitude and direction, sketch each of the following vector functions: (a) iy + jx, (b) (i + j)/√2 I don't understand the notation. Why is there an y and x next to the i and j in...
3. Stuck on a few Vector homework problems

I'm stuck on a few Vector homework problems. I don't quite understand how to write vectors A+B and A-B for questions 1b and 2b. I tried starting with calculating the magnitude for vector A+B on question 1b and then followed by finding theta, but I'm not sure if that's what I'm supposed to do...
4. Vectors physics homework -- Addition of two vector forces

Trying to solve it
5. Vectors Homework

Can’t seems to find the degree
6. I Why is there a contradiction?

Let: $\nabla$ denote dell operator with respect to field coordinate (origin) $\nabla'$ denote dell operator with respect to source coordinates The electric field at origin due to an electric dipole distribution in volume $V$ having boundary $S$ is: \begin{align} \int_V...
7. How do I show that 2 moving objects collide?

They collide when their positions are the same, so I plugged the information for the boat into equation 1 to get an expression for d which is (2i, +j)t^2 Then I used equation 4 to get an expression for d for the branch, which is (-4i, +j)t I would need to take into account the different...
8. Relative Velocity Of Swimmer

So I was just wondering if someone could check my method for (b) as sometimes I can have a tendency of getting the relative components wrong ect. Diagram 1 (a) Time for PY: $T=L/c$ Time for YP: $T=L/c$ Total Time:$2L/c$ (b) Velocity for PY: $c-v$...
9. Find the incorrect relation from the figure

I tried making B vector in direction of D vector with a minus sign and after doing so I got the answer C vector - D vector= -A vector. But it's given as incorrect. I don't know why. Please explain how other options are correct.
10. I Confusion about index notation and operations of GR

Hello, I am an undergrad currently trying to understand General Relativity. I am reading Sean Carroll's Spacetime and Geometry and I understand the physics (to a certain degree) but I am having trouble understanding the notation used as well as the ideas for tensors, dual vectors and the...
11. Intuition behind dot product

I know that a dot product of 2, 2 dimension vectors a, b = (ax * bx) + (ay * by) but it also is equal to a*bCos(θ) because of "projections". That we are multiplying a vector by the 'scalar' property of the other vector which confuses me because that projection is in the direction of the...
12. I Vector math (small angle approximation)

Given the following vectors: how can i determine that Θ = Δp/p ? I can understand that p + Δp = p' but nothing arrives from this. Any help is welcome!
13. Calculating a force on a member (Statics)

I isolated the member ABC and drew the free body diagram: α is then calculated using inverse tan: Tan-1=(6.25+15)/50=23.03 Then force of member BD on the joint can be found by sum of all moments around point A. Then Ax is calculated which is equal to BD×Cos(α)=235.2×Cos(23.03) Ax=216.48...
14. Vectors and vector addition

1. Homework Statement Calculate |u+v+w|, knowing that u, v, and w are vectors in space such that |u|=√2, |v|=√3, u is perpendicular to v, w=u×v. 2. Homework Equations |w|=|u×v|=|u|*|v|*sinΘ 3. The Attempt at a Solution Θ=90° |w|=(√2)*(√3)*sin(90°)=√(6) Then I tried to use u={√2,0,0}...
15. Vectors and scalar projections

1. Homework Statement Let a and b be non-zero vectors in space. Determine comp a (a × b). 2. Homework Equations comp a (b) = (a ⋅ b)/|a| 3. The Attempt at a Solution comp a (a × b) = a ⋅ (a × b)/|a| = (a × a) ⋅b/|a| = 0 ⋅ b/|a| = 0 Is this the answer? Or is there more to it?
16. Finding the expression for the x-component of velocity (vectors?)

1. Homework Statement a particle's position is the vector r=(ct^2-2dt^3)i+(4ct^2-dt^3)j where c and d are positive constants. find the expression for the x-component of the velocity (for time t>0) when the particle is moving in the x-direction. you should express your answer in terms of...
17. Finding an area of a triangle formed by three points

1. Homework Statement P(3, 0, 3), Q(−2, 1, 5), R(6, 2, 7) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR 2. Homework Equations A = \frac{1}{2}|\vec{AB}\times\vec{AC}| Source...
18. Courses Is it okay to not understand the calculus in intro physics?

I don't understand a good portion of the non-algebraic math behind much of the physics in my first semester college class. I understand everything with algebra, and can solve all problems, but I don't understand the relationships with vector cross/dot products, calculus derivations, DE, etc...
19. B The definition of “vector” in math and physics

I'm learning APL and this is how a vector is defined https://tryapl.org: All data resides in arrays. An array is a rectangular collection of numbers, characters and arrays, arranged along zero or more axes. We can use more specific terms for some arrays, like a single number is a scalar, a list...
20. How do you find the acceleration needed to clear a jump?

1. Homework Statement 2. Homework Equations 3. The Attempt at a Solution I used Pythagorean theorem to find the length of the ramp (25^2+18^2 = √949) and found the angle of elevation using tangent (Tanθ=18/25) but then got stuck on what formula to use.
21. Vector Addition Question: find angle (A+B & A-B)

1. Homework Statement Two vectors A and B have precisely equal magnitudes. For the magnitude of A + B to be 65 times greater than the magnitude of A - B, what must be the angle between them? 2. Homework Equations 3. The Attempt at a Solution I tried using the dot product and solving for...
22. B Directions of Vectors

What's the difference between saying that a vector's direction is north of east and north east?
23. Defining which cyclist profits the most from slipstream

1. Homework Statement - Question: Which cyclist (A, B or C) profits the most from cyclist slipstream (also called “aerodynamic drafting”)? - Given: the direction of the wind, the positions of each cyclist; an illustration representing this - NOTE that I am expected to solve this question...
24. Vector torque problem: Force applied to a disc

1. Homework Statement A force of magnitude 50N is applied at the bottom point Q of a disk of radius 8m that is pinned at P (leftmost point) See attached picture (a) Find the angle between the force and the vector from P to Q. (b) Find the magnitude of the applied torque. 2. Homework...
25. Extending an aircraft landing gear that has gotten stuck

Imagine an aircraft of which the its wing is connected to its landing gear by means of a hinge (joint), and then the gear suddenly gets stuck midway. If, subsequently, the aircraft makes a turn around its longitudinal axis (see picture), it seems to hold true that then the angle between the...
26. B Effect of angle on force

Hi, If 2 people are holding a bag at an angle of 45 degrees each, and then only person is going to hold it, it is being said that the force that will have to be applied by that one person will be 1.5 times greater than when he was applying it together with the other. Can anyone explain this or...
27. Resolution of vectors for problems related to mechanics

1. Homework Statement Refer the given image. [Prob 2.9] 2. Homework Equations F=ma 3. The Attempt at a Solution I drew the normal vector perpendicular to the surface of the cone and resolved it as $Nsin\theta=mg$ $Ncos\theta=\frac {mv_{0}^2} {r}$ where $v_{0}$ and $r$ are the speed...
28. B Addition of Perpendicular Vectors in two ways

I have a Force Vector = 100N, making an Angle = 45 degrees with x-axis. When I find their Components trigonometrically, I get 70N each; as Fx = 100xCos(45) = 70N Fy = 100xSin(45) = 70N Verifying the result, by Head-to-Tail method, I get 70N + 70N = 140N. Why is there discrepancy or where am I...
29. B Direction of angular velocity

Angular velocity is the rate of angular displacement about an axis. Its direction is determined by right hand rule. According to right hand rule, if you hold the axis with your right hand and rotate the fingers in the direction of motion of the rotating body then thumb will point the direction...
30. I Kinematics in General?

So, if kinematics is the study of motion without reference to its causes (which is how it seems to be defined in many places), then here is my attempt to come up with a complete picture of motion without reference to its causes. This is just a summary to help me organize my thoughts (it is NOT...