1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Check if answers are right on my review? (vector eqns, curvature )

  1. Mar 31, 2013 #1
    Hi these are questions from my test review that i am unsure of, i posted question and my answer

    if you can tell me if ive gotten right answer that would be much appreciated!

    Let C be the curve with the equations [itex] x = 2 - t^3, y = 2t - 6, z = \ln(t)[/itex]

    Find the point where C intersects the xz-plane
    Find parametric equations of the tangent line at (1,-4,0)

    ans:
    [itex]
    (-25,0,ln(3))
    [/itex]

    [itex]
    x = 1 - 3t, y = -4 + 2t, z = t
    [/itex]

    =========================================


    find an equation of the osculating plane of the curve [itex] x = \sin{5t}, y = \sqrt{5}t, z = \cos{5t} [/itex] at the point [itex] (0,\pi \sqrt{5}, -1)[/itex]

    ans:

    [itex]-\frac{\sqrt{6}}{6} \cos{5t} x + \frac{\sqrt{30}}{6} ( y - \frac{\pi \sqrt{5}}{5}) + \frac{\sqrt{6}}{6} \sin{5t} (z + 1) = 0[/itex]


    =========================================


    Find the curvature of the curve [itex]y = 2 \sqrt{x} [/itex] at the point [itex](3, 2\sqrt{3})[/itex]

    ans:

    [itex]\kappa(3) = \frac{1}{16}[/itex]

    =========================================

    An athlete throws a shot at an angle of 45 degrees to the horizontal at an initial speed of 36 ft/sec. It leaves his hand 4 feet above the ground.

    Where is the shot 2 seconds later?
    Where does the shot land?

    ans:

    [itex](36\sqrt{2} ft, 36\sqrt{2} - 15.6 ft)[/itex]

    x = 132ft

    =========================================


    Find the tangential and normal components of the acceleration vector of a particle with position function [itex] r(t) = \cos{t} i + \sin{t} j + \sqrt{15}t k[/itex]


    ans:

    at = 0
    an = 1


    ==========================================

    True/false...

    The curve [itex]r(t) = <0,t^2, 4t>[/itex] is a parabola

    T

    The curve with the vector equation [itex]r(t) = t^3 i + 2t^3j + 3t^3 k[/itex] is a line

    T

    The binormal vector is [itex]B(t) = N(t) x T(t)[/itex]

    F (opposite direction... not sure about this one though)

    If curvature [itex]\kappa(t) = 0[/itex] for all t, the curve is a straight line

    T

    The curve [itex]r(t) = <2t, 3 - t, 0 > [/itex] is a line that passes through the origin.

    F

    If [itex]|r(t)| = 1[/itex] for all t, the r'(t) is orthogonal to r(t) for all t

    T

    if u(t) and v(t) are differentiable vector functions then [itex]\frac{\delta}{\delta t}[u(t) x v(t)] = u'(t) x v'(t)[/itex]

    F


    I'm pretty sure the majority of these are right. the physics one and oscillating plane are the ones im kind of unsure of! thanks for any help i have test soon!
     
    Last edited: Mar 31, 2013
  2. jcsd
  3. Apr 1, 2013 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    This can't be correct. There cannot be a "t" in the equation.

     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Check if answers are right on my review? (vector eqns, curvature )
Loading...