Answer to Question #155904 in Classical Mechanics for Galaxy

Question

1. A rocket has an initial mass of 2 x 104 kg, a mass ratio of 3, a burning rate of 100 kg/sec, and an exhaust velocity of 980 m/sec. The rocket is fired vertically from the surface of the earth. How long after ignition of the engines will the rocket leave the ground?  (R1P14-3, 493)

Answer 1

Answer

For rocket impulsive force and it's weight equation is given by

$v\frac{dm}{dt}=(m_0-\frac{dm}{dt}) g$

Putting all given values

$980\times100=( 2 \times10^4 -100t) \times9.8$

Now solving above equation

$100t=( 2 \times10^4 - 10^4 ) sec$

The time after ignition of the engines will the rocket leave the ground

t=100sec.