A rocket weighing 500 kg is at rest initially. When the jets fire up it rises to 300 m and the speed is increased to 300 km/h in 20 seconds. What is the total work and power?
A rocket with mass 500 kg is initially rest. It takes off, and 20 seconds later reaches a height of 300 m and is traveling at 300 km/h. At the new position of the rocket there is an increase in its potential energy as well as kinetic energy.
At the point the rocket is at after 20 seconds, its gravitational potential energy is equal to `PE = m*g*h` = 500*9.8*300 = 1470000 J. The kinetic energy of the rocket is equal to `KE = (1/2)*m*v^2` = `(1/2)*500*(300*(1000/3600))^2` = 1736111.111 J
The increase in the total energy of the rocket is due to the work done on it. This is equal to the sum of the increase in kinetic energy and the increase in the potential energy. The work done on the rocket is equal to 3206111.111 J
As it takes 20 seconds for the rocket to reach this stage, the power of the jets is 160305.5556 W