A child of mass 53.7 kg sits on the edge of a merry-go-round with radius 2.2 m and mo- ment of inertia 205.327 kgm2. The merry- go-round rotates with an angular velocity of 1.6 rad/s. The child then walks towards the center of the merry-go-round and stops at a distance 0.836 m from the center. Now what is the angular velocity of the merry-go-round? Answer in units of rad/s.

In this thread, i would like you to comment on the nature of light and how operation of telescopes. light has a duality of a particle and a wave; which one affects your life? also how does light interact with optics inside telescopic systems? answer these questions in two paragraphs. then respond the another students response.

Aleaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.) lim n → ∞ n (9.8)(45−3 xi) i = 1 δx express the work as an integral. 0 dx evaluate the integral. (round your answer to the nearest integer.) j

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?