A two-stage rocket has a total initial mass with the fuel of 4.5x106 kg is docked...

A two-stage rocket has a total initial mass with the fuel of 4.5x10⁶ kg is docked at rest at a space station. A total of 2.3x10⁶ kg of fuel is on board. The mission for the ship is to reach a planet that is located at a distance of 7.5x10¹⁰m away. The fuel is used at a constant rate of 800kg/s for both stages of the rocket. The exhaust velocity for the rocket's engines is 7500m/s (stage1) and 5000m/s (stage2). The mass of stage 1 (bottom half) is 0.75x10⁶kg without fuel after stage 1 is complete, stage 2 the ignites and accelerates the rocket until the fuel runs out. Assume all the motion takes place in one dimension and the gravitational force can be neglected.

1. The fuel allocated for the 1st stage is 1.5x10⁶kg but only 1.25x10⁶ kg is used. The rest remains on stage1. The fuel for the second stage is 0.8x10⁶kg. What is the speed of the rocket when stage 2 is complete?

2. How much faster or slower would you be going if you use all 2.3x10⁶kg of the rocket's fuel during stage 1 and didn't use the second stage?

3. Some fuel was left on stage 1 which is used to alter its velocity so that it can return to the space station. If you were to rotate stage 1 so that the exhaust point in the opposite direction, do you have enough fuel to return stage1 to the space station? What is the final velocity of the rocket? If not, what would the minimum exhaust velocity of stage one need to be adjusted to in order for the rocker to make it back?

Expert Solution

genius_generous answered 2 years ago

A rocket has an initial mass of 28500 kg, of which 20% is the payload (i.e.,...

A rocket has an initial mass of 28500 kg, of which 20% is the payload (i.e., the mass of the rocket minus the fuel). It burns fuel at a rate of 195 kg/s and exhausts its gas at a relative speed of 1.5 km/s. (a) Find the thrust of the rocket. kN (b) Find the time until burnout. s (c) Find its final speed assuming it moves upward near the surface of the earth where the gravitational field g is...

A 785-kg two-stage rocket is traveling at a speed of 6.30

In the first stage of a two-stage rocket, the rocket is fired from the launch pad...

In the first stage of a two-stage rocket, the rocket is fired from the launch pad starting from rest but with a constant acceleration of 3.50 m/s2 upward. At 25.0 s after launch, the second stage fires for 10.0 s, which boosts the rocket’s velocity to 132.5 m/s upward at 35.0 s after launch. This firing uses up all the fuel, however, so after the second stage has finished firing, the only force acting on the rocket is gravity. Air...

4.15 A small 7.40-kg rocket burns fuel that exerts a time-varying upward force on the rocket....

4.15 A small 7.40-kg rocket burns fuel that exerts a time-varying upward force on the rocket. This force obeys the equation F=A+Bt2. Measurements show that at t=0, the force is 104.0N , and at the end of the first 1.50s , it is 193.0N . Find the constant A Find the constants B Find the net force on this rocket the instant after the fuel ignites. Find the acceleration of this rocket the instant after the fuel ignites. Find the...

A rocket has a mass of 1.40×04 kg and its engine has a thrust of 200×105...

A rocket has a mass of 1.40×04 kg and its engine has a thrust of 200×105 N. If its engines fire in the vertical direction for 1 min starting from rest, to what vertical height would it rise in the absence of air resistance? (To simplify things, assume the mass is constant. However, in reality the mass of rockets decreases substantially while rising)

A rocket is launched straight up. It contains two stages (Stage 1 and Stage 2) of...

A rocket is launched straight up. It contains two stages (Stage 1 and Stage 2) of solid rocket fuel that are designed to burn for 10.0 and 5.0 s, respectively, with no time interval between them. In Stage 1, the rocket fuel provides a net upward acceleration of 18 m/s2. In Stage 2, the net upward acceleration is 13 m/s2. Neglecting air resistance, calculate the maximum altitude above the surface of Earth of the payload and the time required for...

2. A spacecraft of initial mass M (including the mass of the fuel) is at rest...

2. A spacecraft of initial mass M (including the mass of the fuel) is at rest in the solar system, preparing to disembark on a grand mission to Alpha Centauri. Its engines work by combining matter and antimatter and directing the hard gamma rays that result out the spacecraft’s rear. The engines fire for a brief time, bringing the ship’s speed to v = 0.95 with respect to the solar system. a) What is the rest mass m of the...

A 790-kg two-stage rocket is traveling at a speed of 6.60×103 m/s away from Earth when...

A 790-kg two-stage rocket is traveling at a speed of 6.60×103 m/s away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of 2.80×103 m/s relative to each other along the original line of motion What is the speed of each section (relative to Earth) after the explosion? Express your answers using three significant figures separated by a comma. V1,V2= What are the direction of each section (relative...

A 720-kg two-stage rocket is traveling at a speed of 6.90×10^3 m/s away from Earth when...

A 720-kg two-stage rocket is traveling at a speed of 6.90×10^3 m/s away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of 2.10×10^3 m/s relative to each other along the original line of motion.What is the speed of each section (relative to Earth) after the explosion? R/= v1=5850, v2=7950. How much energy was supplied by the explosion? [Hint: What is the change in kinetic energy as a...

You have a rocket with a mass of 2.5kg, that provides a total forward force of...

You have a rocket with a mass of 2.5kg, that provides a total forward force of F=49N. a.) At what angle must you launch it so that it flies perfectly horizontally. b.) Now you set it up to launch vertically. From rest it takes off but it only has enough fuel to burn for 10 seconds. How high does it get? c.) If it launched at 45 degrees, the fuel burnt for 10 seconds, then it fell to the ground,...

Question