1. A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) ism, the fuel is consumed at rater, and the exhaust gases are ejected with constant velocityv_e(relative to the rocket). A model for the velocity of the rocket at timetis given by the equation

v(t) =gtv_eln(mrt/m)

wheregis the acceleration due to gravity andtis not too large. Ifg= 9.8 m/s², m=29,000kg, r=190kg/s, andv_e=3,100m/s,

find the height of the rocket (in meters) one minute after liftoff. (Round your answer to the nearest whole meter.)

2. Find the volume of the solid obtained by rotating about thex-axis the region enclosed by the graphs ofy=4/x^2+4, y=0, x= 0, andx=2.