Acylindrical rocket of diameter 2.r, mass m, and containing fuel of mass m, is moving through empty space at velocity vu. at some point the rocket enters a unifom cloud of interstellar particles with volume density n (e g. particles/m), each particle having the mass m < ms and initially at rest. to compensate for the dissipative force of the particles colliding with the rocket, the rocket engines emit fuel at the rate y with dm, /dr =-7 at a constant velocity u with respect to the rocket. ignore gravita- tional interaction between the rocket and the cloud particles. 1. assuming that the dissipative drag force from the cloud particles is -av, where a is a constant, derive the differential equation for the velocity vi) of the rocket through the cloud as it is firing its engines 2. what must the rocket thrust yu be to maintain the constant velocity u7 3, if the rocket suddenly runs out of fuel, how would its velocity vn) decrease with time as the rocket moves through the cloud. 4. bonus: assuming that each cloud particle bounces off the rocket elastically, and collisions occur very frequently, prove that the drag force is indeed proportional to v and estimate the constant a, if the front nose-cone of the rocket has the opening angle of 90 n particles/m tg

i would think it's food chain

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

-it's clean and sustainable

-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

-almost everywhere, the shallow ground or upper 10 feet of the earth's surface maintains a nearly constant temperature between 50° and 60°f (10° and 16°c)

-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

-in the winter, the heat pump removes heat from the heat exchanger and pumps it into the indoor air delivery system

-in the summer, the process is reversed, and the heat pump moves heat from the indoor air into the heat exchanger

-the heat removed from the indoor air during the summer can also be used to provide a free source of hot water

the answer is a. hope this .

there are no atoms