In a region of space there exists the following electric field (in spherical coordinates) : E~ (r, θ, φ) = (3r 2 cos(θ)ˆr − r 2 sin(θ) θˆ) N m2C Find the amount of charge contained in the region of spaces described by the upper (z ≥ 0) hemisphere of a sphere radius 50cm centered at the origin. Do this two ways, making use of: a) The integral form of Gauss’s law b) The differential form of Gauss’s law

Two manned satellites approaching one another at a relative speed of 0.550 m/s intend to dock. the first has a mass of 2.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. assume that the positive direction is directed from the second satellite towards the first satellite. (a) calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest.(b) what is the loss of kinetic energy in this inelastic collision? (c) repeat both parts, in the frame of reference in which the second satellite was originally at rest. final velocity(d) loss of kinetic energy = ?