A ball is thrown straight upward. Neglecting air resistance, what initial up-
ward speed does the ball need in order to remain in the air for a total time of 10 sec be- fore it is caught at the initial point of release?

Find v(t), given acceleration a(t)=7j and initial velocity v(0)=k

What is the role of lenses in microscopy?

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants