Recent content by Insolite

Question: For the scalar field \Phi = x^{2} + y^{2} - z^{2} -1, sketch the level surface \Phi = 0 . (It's advised that in order to sketch the surface, \Phi should be written in cylindrical polar coordinates, and then to use \Phi = 0 to find z as a function of the radial coordinate \rho)...

Aah, thanks a lot for your help, I've got it now. (:

A scalar field \psi is dependent only on the distance r = \sqrt{x^{2} + y^{2} + z^{2}} from the origin. Show: \partial_{x}^{2}\psi = \left(\frac{1}{r} - \frac{x^{2}}{r^{3}}\right)\frac{d\psi}{dr} + \frac{x^{2}}{r^{2}}\frac{d^{2}\psi}{dr^{2}} I've used the chain and product rules so...

Question: A cannon, located ##60.0 m## from the base of a vertical ##25.0 m## tall cliff, shoots a ##15 kg## shell at ##43.0°## above the horizontal toward the cliff. What must the minimum muzzle velocity be for the shell to clear the top of the cliff? I have attempted a solution that I'm...

A spaceship is measured to be 50m long in it's own rest frame takes ##1.50 \times 10^{-6} s## to pass overhead, as measured by an observer on earth. What is its speed relative to earth? My attempt at the solution involves the use of the equation for length contraction, ##l = l_{0}\sqrt{1 -...

Hi, thankyou for your response. I had approached the problem this way previously, but for some reason or another I discarded it. I have tried to run it through and have calculated what I think is a reasonable answer - ##t_{2} = \sqrt{\frac{2h}{g}}## ##t_{1} = \sqrt{\frac{3h}{2g}}##...

Question: "A man steps from the top of a tall building. He falls freely from rest to the ground, a distance of h. He falls a distance of h/4 in the last 0.800 s of his fall. Neglecting air resistance, calculate the height h of the building. I've attempted the solution in a number of different...