Chapter 8, Problem 39P

The upward velocity of a rocket can be computed by the following formula:

$v=u\text{In}\frac{m_0}{m_0-qt}-gt$

where $v=$ upward velocity, $u=$ the velocity at which fuel is expelled relative to the rocket, $m_0=$ the initial mass of the rocket at time $t=0,q=$ the fuel consumption rate, and $g=$ the downward acceleration of gravity $\left(\text{assumed constant }=9.81\text{m}/{\text{s}}^2\right)$. IF $u=2200\text{m}/\text{s,}{m}_0=160,000\text{ kg, and }q=2680\text{kg}/\text{s},$ compute the time at which $v=1000\text{m}/\text{s}$. (Hint: t is somewhere between 10 and 50 s.) Determine your result so that it is within 1% of the true value. Check your answer.