Achild's toy consists of a spherical object of mass 50 g attached to a spring. one end of the spring is fixed to the side of the baby's crib so that when the baby pulls on the toy and lets go, the object oscillates horizontally with a simple harmonic motion. the amplitude of the oscillation is 6 cm and the maximum velocity achieved by the toy is 3.2 m/s . what is the kinetic energy k of the toy when the spring is compressed 5.1 cm from its equilibrium position?

You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. you will have no access to any electricity, but you must be able to illuminate the entire grounds. you know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. suppose the intensity is 90 when the distance is 5 m. a. write an equation to model the situation. b. solve for the constant of variation. c. write the equation to model the situation using the constant () of variation. d. you have been given lanterns with 40 light intensity. use your equation to solve for the distance from the lantern. e. you need to illuminate 225 km. how many meters do you need to light? f. how many lanterns will you need?