If the rocket burns its fuel in a time of 50.0 s and the relative speed of the exhaust gas is vex = 2100 m/s, what must the mass ratio m0/m be for a final speed v of 8.00 km/s (about equal to the orbital speed of an earth satellite)?

Acarpenter is driving a 15.0-g steel nail into a board. his 1.00-kg hammer is moving at 8.50 m/s when it strikes the nail. half of the kinetic energy of the hammer is transformed into heat in the nail and does not flow out of the nail. what is the increase in temperature of the nail after the three blows that the carpenter needs to drive the nail in completely? the specific heat of steel is 448 j/kg ∙ k. a) 2.7 k b) 1.8 k c) 7.7 k d) 8.1 k e) 3.6 k