Suppose that a large, very dense asteroid with mass one hundredth (1/100) of that of the earth collides with our planet. assume that the asteroid hits the equator with a speed of 1000 km/s, that it comes in on a purely radial path, and that it stays near the surface of the earth after the collision. how long is an earth-day after the collision? (you can assume that earth has mass m = 6 × 1024 kg and radius r = 6400 km and has the shape of a perfect sphere).

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?