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.

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

An object resting on a table weighs 100 n. with what force is the object pushing on the table? with what force is the table pushing on the object? explain how you got your answer.

Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. the astronaut has her lucky penny in her hand behind her back as the space pirates break into the control room. she has just locked the controls so that the ship is accelerating in the direction of the control room’s ceiling. simon wants the astronaut to use the penny to hit a button on the control panel to turn off the lights and escape. the button is located a short distance behind and below the astronaut’s hands. how should simon use the theory of relativity to describe what the astronaut must do in order to hit the button?