1. ### How to find d2 when given d1 and d, total time, and average velocity?

I rearranged the displacement formula to d2 = d + d1. I used cosine law to solve for d2 since the triangle is not right-angled but I am not getting the correct answer or angle for d2. The angle I used in cosine law (based on the diagram) was 32+12+90 = 134. d = v(t) = 130(3) = 390 km/h [N 32 E]...
2. ### Physics lab report calculating resultant forces -- help please

i have attached my attempt above i have sent it to my teacher and he said i should fix the mistakes and resend it
3. ### Calculate the dual basis and tangent basis vectors

a) Since ##tan(x/x_0)## is not defined for ##x=\pm\pi/2\cdot x_0## I assume x must be in between those values therefore ##-\pi/2\cdot x_0 < x < \pi/2\cdot x_0## and y can be any real number. Is this the correct answer on a)? b) I can solve x and y for s and t which gives me ##y=y_0\cdot s## and...
4. ### I Scalar product of biharmonic friction with velocity components

I know that taking the scalar product of the harmonic (Laplacian) friction term with ##\underline u## is $$\underline u \cdot [\nabla \cdot(A\nabla \underline u)] = \nabla \cdot (\underline u A \nabla \underline u) - A (\nabla \underline u )^2$$ where ##\underline u = (u,v)## and ##A## is a...
5. ### I Principal difference between complex numbers and 2D vectors revisited

I know this topic was raised many times at numerous forums and I read some of these discussions. However, I did not manage to find an answer for the following principal question. I gather one deals with the same set in both cases equipped it with two different structures (it is obvious if one...
6. ### I Translational and rotational velocity

For a cylinder rolling down an inclined plane, does the tangential velocity of a point a distance R from the axis of rotation equal the velocity of the center of mass?
7. ### 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)##...
8. ### 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...
9. ### 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...
10. ### Vectors physics homework -- Addition of two vector forces

Trying to solve it
11. ### Vectors Homework

Can’t seems to find the degree
12. ### 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...
13. ### 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...
14. ### 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##...
15. ### 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.
16. ### 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...
17. ### 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...
18. ### 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!
19. ### 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...
20. ### Vectors and vector addition

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. Homework Equations |w|=|u×v|=|u|*|v|*sinΘ The Attempt at a Solution [/B] Θ=90° |w|=(√2)*(√3)*sin(90°)=√(6) Then I tried to use u={√2,0,0}...
21. ### Vectors and scalar projections

Homework Statement Let a and b be non-zero vectors in space. Determine comp a (a × b). Homework Equations comp a (b) = (a ⋅ b)/|a| The Attempt at a Solution [/B] 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?
22. ### Finding the expression for the x-component of velocity (vectors?)

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 variables...
23. ### Finding an area of a triangle formed by three points

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 Homework Equations A = \frac{1}{2}|\vec{AB}\times\vec{AC}| Source...
24. ### 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...
25. ### 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...
26. ### How do you find the acceleration needed to clear a jump?

Homework Statement Homework Equations 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.
27. ### Vector Addition Question: find angle (A+B & A-B)

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? Homework Equations The Attempt at a Solution I tried using the dot product and solving for the angle but...
28. ### B Directions of Vectors

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

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...
30. ### Vector torque problem: Force applied to a disc

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. Homework Equations...