Avery long stick ruled with meter markings is placed in empty space. a spaceship of rest length l = 100 m runs lengthwise alongside the stick. two space travelers equipped with knives and synchronized watches station themselves fore and aft. at a prearranged time, each reaches through a porthole and slices through the stick. if the relative velocity of the stick and ship is v = (4/5)c, how many meter marks are on the cut-off portion of the stick? do the calculation first in the frame of the ship, and then do the calculation over in the frame of the stick. in each case, draw careful pictures.

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?