An asteroid with a diameter of 10 km and a mass of 175 times

An asteroid with a diameter of 10 km and a mass of 1.75 times 10^15 kg impacts the earth at a speed of 30.1 km/s, landing in the Pacific Ocean. If 4.25% of the asteroid\'s kinetic energy goes to boiling the ocean water (assume an initial water temperature of 10.0^degree C), what mass of water will be boiled away by the collison? (For comparison, the mass of water contained in Lake Superior is about 2. times 10^15 kg.)_______kg

Solution

KE of the asteroid is K = 0.5*m*v^2 = 0.5*1.75*10^15*30100^2 = 7.92*10^23 J

4.25% of KE is E = 0.0425*7.92*10^23 = 3.36*10^22 J

heat energy required by water to boil is mw*s_w*dT = 3.36*10^22

dT = 100-10 = 90 C

S_w = 4186 J/Kg-K

mw*4186*90 = 3.36*10^22

mass of water is 8.918*10^16 kg