Chapter 2.2, Problem 44ES

The accompanying figure shows the velocity versus time curve for a rocket in outer space where the only significant force on the rocket is from its engines. It can be shown that the mass $M\left(t\right)$ (in slugs) of the rocket at time $t$ seconds satisfies the equation

$M\left(t\right)=\frac{T}{dv/dt}$

where $T$ is the thrust (in lb) of the rocket’s engines and v is the velocity (in ft/s) of the rocket. The thrust of the first stage of a Saturn $V$ rocket is $T=7,680,982\text{ lb}$ . Use this value of $T$ and the line segment in the figure to estimate the mass of the rocket at time $t=100$ .