Question

Mass of spacecraft varies with time as $m=5000e^{-t}\text{kg}$. Find the rate of fuel ejection after $5\text{s}$. (Take $e=2.718$)

• A. $23.7\text{kg/s}$
• B. $33.7\text{kg/s}$
• C. $337\text{kg/s}$
• D. $237\text{kg/s}$

Answer 1

The correct option is B $33.7\text{kg/s}$

Given, $m=5000e^{-t}$
Rate of fuel ejection $\left(\mu \right)=\left|\frac{dm}{dt}\right|$
$\mu =\left|\frac{dm}{dt}\right|=5000e^{-t}$
$\Rightarrow \mu =\frac{5000}{e^5}=33.7\text{kg/s}$