q01 - Physics 3221 Mechanics I Fall Term 2010 Quiz 1 This...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 3221 Mechanics I Fall Term 2010 Quiz 1 This is a 20 min. quiz (closed book). There are two problems (the second problem is on the back). Problem 1. [2 pts] Find the gradients of the two functions u(x, y ) = x + y2 , x v (x, y ) = y + and show that they are always orthogonal. Solution. ∇u = 1 − y y2 e1 + 2 e2 2 x x x x2 ∇v = 2 e1 + 1 − 2 e2 y y ∇u · ∇v = 0 ⇒ 1 ∇u ⊥ ∇v x2 , y Problem 2. [3 pts.] The position vector of a point particle is given by r(t) = (3t2 − 4) e1 + t3 e2 + (t + 3) e3 . (a) find the velocity v (t), the acceleration a(t) and the speed v (t) of this particle. (b) find the time derivative of the vector r × v, i.e. find d (r × v ) dt Solution. (a) v(t) = 6te1 + 3t2 e2 + e3 a(t) = 6e1 + 6te2 |v(t)| = √ 36t2 + 9t4 + 1 (b) d (r × v ) = v × v + r × a = r × a = −6t(t + 3)e1 + 6(t + 3)e2 + 12t(t2 − 2)e3 dt 2 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern