In a rocket-propulsion problem the mass is variable. another such problem is a raindrop falling through a cloud of small water droplets. some of these small droplets adhere to the raindrop, thereby increasing its mass as it falls. the force on the raindrop is
fext=dpdt=mdvdt+vdmdt
suppose the mass of the raindrop depends on the distance x that it has fallen. then m=kx, wherek is a constant, and dm/dt=kv. this gives, since fext=mg,
mg=mdvdt+v(kv)
or, dividing by k,
xg=xdvdt+v2
this is a differential equation that has a solution of the form v=at, where a is the acceleration and is constant. take the initial velocity of the raindrop to be zero.
a) using the proposed solution for v, find the acceleration a.
b) find the distance the raindrop has fallen in
t = 2.00s .
c) given that
k = 2.00g/m , find the mass of the raindrop at t = 2.00s

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

-the first industrial use of geothermal energy began near pisa, italy in late 18th century

-in 1904, italian scientist piero ginori conti invented the first geothermal electric power plant in which steam was used to generate the power

-with the above experiment, the first geothermal plant in usa started in 1922 with a capacity of 250 kilowatts

-however, in 1946 first ground-source geothermal heat pump installed at commonwealth building in portland, oregon

-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

-as effect of climate change started showing results, governments of various countries joined hands to fight against it, for which kyoto protocol was signed in japan in 1997, laid out emission targets for rich countries and required that they transfer funds and technology to developing countries, 184 countries have ratified it

hope this