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  1. Z

    Projections in Linear Algebra

    I'm fairly sure I'm right about the column space but I could use an explanation on perpendicular matrices if anyone can help.
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    Projections in Linear Algebra

    Homework Statement Some of the details in this question are based off the use of matlab. If it's needed I can show the matrices that MATLAB creates. Let A = magic(8); A = A(:,1:3) and let S be the Column Space of A. For b = [1:8]' compute the projection of b onto the Column Space of A...
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    Accceleration due to gravity of a Black Hole

    So, the solution to this problem was posted on my course website, but I'm still having issues. Basically, the answer is the same as mine until: a_{0} = \frac{c^{4}}{4(1+\epsilon)^{2}GM} The (1+ε)2 is simplified as (1+2ε)... ok, if ε is really small, I suppose assuming ε2 = 0 is alright. But...
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    Accceleration due to gravity of a Black Hole

    If there is anyone who could at least give me a point in the right direction I'd be grateful.
  5. Z

    Accceleration due to gravity of a Black Hole

    Homework Statement The radius Rh and mass M of a black hole are related by Rh = \frac{2GM}{c2}, where c is the speed of light. Assume that the gravitational acceleration ag of an object at a distance ro = (1 + ε)Rh from the center of a black hole is given by ag = \frac{GM}{r2}, where ε is a...
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    Roational Mechanics of Helicopter Blades

    Scratch that... I get the correct answers according to the book, but using the numbers from online I get the wrong answers... makes no sense to me
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    Roational Mechanics of Helicopter Blades

    Right, rotated about it's end the moment of inertia is I = (m L2) /3 I was assuming that the rotational axis is in the center of the blade though, leading to my equation. Using I = (m L2) /3 actually leads to correct answers. Thanks ^^
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    HW problem with force and friction

    Solving for T, I got 76.97 N I'm willing to bet the discrepancy is rounding. To be sure, I used mg-Tsin(θ) = N friction = (mg-Tsin(θ))μ Tcos(θ)=friction = (mg-Tsin(θ))μ T(cos(θ) + sin(θ)μ) = mgμ so, T =mgμ/(cos(θ) + sin(θ)μ)
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    Uniform Circular motion

    The first thing to do is to make a picture. You'll notice that there are only 2 forces acting on the plane. Namely, tension and gravity. You know that the horizontal motion is circular, so that leads to Fnet = mv^2/r You know Fnet in the x direction, and velocity. Find a relationship to...
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    Roational Mechanics of Helicopter Blades

    This question is still getting the better of me if anyone could help.
  11. Z

    Roational Mechanics of Helicopter Blades

    Homework Statement A uniform helicopter rotor blade is 8.82 m long, has a mass of 108 kg, and is attached to the rotor axle by a single bolt. (a) What is the magnitude of the force on the bolt from the axle when the rotor is turning at 302 rev/min? (Hint: For this calculation the blade can...
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    Time Dilation - Help needed

    The idea of time dilation is that light moves at the same constant rate seen from any perspective and that other moving objects don't. As you move faster you're perception of reality has a decreased rate. Everything else appears slower to you. To find the time distortion you would use Einstein's...
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    Vector Addition

    The problem is that you're angle is wrong. Try drawing a small graph with the angle starting from the positive y-axis (north) and going towards the x-axis (east). You see that the 55° angle is made with the y-axis, and not the x-axis.
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    Help finding an angle please?

    The question is asking you to find the angle between the velocity and the line of sight. If you solve both triangles you'll find the angle is the same: tan ^-1 (distance y/ distance x) = tan ^-1 (Vy/Vx) so, the angle between the two is: tan ^-1 (distance y/ distance x) - tan ^-1 (Vy/Vx) = 0
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    Basic Calculus help with finding components

    I appreciate the answer. And, actually, now that I see it, this should've been really obvious. Thank you ^^
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    Basic Calculus help with finding components

    I always seem to find this place whenever I'm in need of homework help, so I finally decided to register (and hopefully post in the right area). My given problem is Here are three displacements, each in meters: d1 = 4.2i + 2.7j - 7.9k, d2 = -1.0i + 2.0j + 3.0k, and d3 = 4.0i + 3.0j +...
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