Work
A rocket's engine ejects fuel at a rate of \( 40 \text{ kg/s} \) with an exhaust velocity of \( 4000 \text{ m/s}. \) If the rocket's initial mass is \( 24000 \text{ kg}, \) what is the approximate change in velocity after \( 24\) seconds?
A rocket whose mass is \( M_i = 2600 \text{ kg}, \) of which \( 2080 \text{ kg} \) is fuel, consumes fuel at a rate of \( R = 26 \text{ kg/s}. \) The exhaust velocity of the fuel relative to the rocket engine is \( v_e = 400 \text{ m/s}. \) If the fuel consumption rate is changed to double the thrust, how long can the rocket fire the engine?
A \( 5000 \text{ kg} \) space shuttle moving toward Moon with velocity \( 100 \text{ m/s} \) fires its rocket engine. The rocket engine ejects exhaust at a speed of \( 300 \text{ m/s} \) relative to engine. If the final speed of the shuttle is \( 130 \text{ m/s}, \) what is the approximate amount of exhaust the shuttle has ejected?
A rocket of mass \( 5000 \text{ kg} \) ejects fuel at a rate of \( R = 5 \text{ kg/s} \) with an exhaust velocity of \( v_e = 3000 \text{ m/s}. \) If the rocket's initial velocity is \( v_i = 1800 \text{ m/s}, \) approximately how long will it take to reach a velocity of \( v_f =2700 \text{ m/s}? \)
A rocket whose initial mass is \( M_i = 1380 \text{ kg} \) consumes fuel at rate of \( R = 22 \text{ kg/s}. \) The exhaust velocity of fuel relative to the rocket engine is \( v_e = 200 \text{ m/s}. \) Find the thrust that the rocket engine provides.