A 0.6-kg model rocket is loaded with 0.7 kg of rocket fuel. After launch, the rocket rises at a constant rate of 4 m/s, but the rocket fuel is dissipated at a rate of 0.15 kg/s. Find the work done in propelling the rocket 16 m above the ground. (Use 9.8 m/s2 for g.) a) Find the work (in J) needed to lift the model rocket itself. (Ignore the work needed to lift the fuel.)
b) Show how to approximate the required work (in J) to lift the rocket fuel by a Riemann sum. (Let x be the distance in meters above the ground. Enter xi* as xi.)
lim
n→∞
c) Express the work (in J) required to lift the rocket fuel as an integral of x (in m).
d) Evaluate the integral (in J).
e) Find the total work (in J) by adding the work of lifting the model rocket to the work of lifting the rocket fuel.