Recent content by DarkSamurai

The best way to setup these problems is first create a table X_initial X_final Vx_initial Vx_final Ax time Y_initial Y_final Vy_initial Vy_final Ay time The two things that we know is that acceleration is going to be 0 in the x-direction in these types of problems (always). And that the...

e_r and e_theta are the unit vectors... for the coordinate system I believe. \hat{e_{r}} and \hat{e_{\theta}}

Homework Statement Convert F into cartesian coordinates from spherical F = -4*theta*e_r + 1e_phi r(t) = 2, theta(t) = 4t, phi(t) = pi / 2 Homework Equations x = rsin(theta)cos(phi) y = rsin(theta)sin(phi) z = rcos(phi) The Attempt at a Solution Where I'm having problem is converting F into...

Homework Statement x = \frac{u^{2} + v^{2}}{2} y = uv z = z Find the arc length given: u(t) = cos(t), v(t) = sin(t), z = \frac{2t^{\frac{3}{2}}}{3} Homework Equations ds^{2} = dx^{2} + dy^{2} + dz^{2} In curvilinear coordinates thhis becomes ds =...

The first part confuses me, "length x makes an angle of theta with the z axis" What does this mean? on the zx plane? So should I take the magnitude and then take the cos of the angle?

Homework Statement The vector u of length 6 makes an angle of 40 with the z axis; it's vector projection on the xy plane makes an angle of 44 degrees with the x axis. The vector projection of a second vector v on the z axis has a length 5. The vector projection of v on the xy plane has a...

Homework Statement Find the arc length of r(t) = cos(t)^3 i + sin(t)^3 j from t = 0 to t = 2 * Pi It's a hypocycloid that's four cusped. Homework Equations s = \int\sqrt{x'^2 + y'^2} The Attempt at a Solution x = cos(t)^3 y = sin(t)^3 x' = -3cos(t)^2*sin(t) y' =...