A charge of +5nC and mass of 10-6 kg is moved a distance of 4 cm against a uniform electric field of magnitude 2·105 V/m from M to N. (a) Calculate the work
done in moving the charge from M to N. (b) The charge is now released and returns
to M. Calculate the kinetic energy of the charge at M and its velocity.

A58-kg boy swings a baseball bat, which causes a 0.140-kg baseball to move toward third base with a velocity of 38.0 m/s.

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

Identify the correct relation showing that the radius r of the orbit of a moon of a given planet can be determined from the radius r of the planet, the acceleration of gravity at the surface of the planet, and the time τ required by the moon to complete one full revolution about the planet. determine the acceleration of gravity at the surface of the planet jupiter knowing that r = 71 492 km and that t= 3.551 days and r= 670.9 × 10^3 km for its moon europa.