1(ke, pe) an object of mass 90 lbm is projected straight upward from the surface of the earth and reaches a height of 900 ft when its velocity reaches zero. the only force acting on the object is the force of gravity. the acceleraton of gravity is g = 32.2 ft/s2 . determine the initial kinetic energy of the object [ft·lbf], and the object’s initial velocity [ft/s].

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