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]...
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...
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...
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...
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?
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)##...
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...
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...
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...
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...
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##...
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.
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...
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...
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...
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}...
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?
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...
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...
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...
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...
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.
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...
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...
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
(leftmost 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...