We can now look at the role of specific impulse in setting the performance of a rocket. 14. . In serial staging, shown above, there is a small, second stage rocket that is placed on top of a larger first stage rocket. Options vary with different browsers. The Rocket Lab Rutherford engines, designed for small orbital rockets like the Electron, use pumps powered by lithium-ion batteries. The collision could pose a threat to life on Earth. If 5500 J is released in the explosion, how much kinetic energy does each piece acquire? This Interactive is intended for use at the middle to later stages of the learning cycle on kinematic graphing. This lesson expands on the traditional activity by adding a second stage to the balloon rocket, modeled after how real rocket launches work (Figure 2). A 725-kg two-stage rocket is traveling at a speed of \({\bf{6}}{\bf{.60 \times 1}}{{\bf{0}}^{\bf{3}}}\;{\bf{m/s}}\) away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of \({\bf{2}}{\bf{.80 \times 1}}{{\bf{0}}^{\bf{3}}}\;{\bf{m/s}}\)relative to each other along the original line of motion. The rocket drops the first stage and continues upward briefly until a time t2 at which point the second stage begins to fire and the rocket again accelerates upward, this time with a larger (but again constant) acceleration. Answer (1 of 2): Rockets get big fast, because for every kilogram of payload you want to add to the rocket, you have to add more fuel to carry that payload, and more fuel to carry that fuel, etc. A two-stage-to-orbit (TSTO) or two-stage rocket launch vehicle is a spacecraft in which two distinct stages provide propulsion consecutively in order to achieve orbital velocity. The equation is given as: v = v e l n m 0 m f = I s p g 0 l n m 0 m f. Where, v: maximum change of velocity of the vehicle. Net Force (and Acceleration) Ranking Tasks, Trajectory - Horizontally Launched Projectiles, Which One Doesn't Belong? Consider the direction of motion of the rocket before the explosion to be the positive direction, i.e., direction away from the Earth to be positive. Sometime during this second period of acceleration, our recording apparatus stops. The Two-Stage Rocket Interactive is a simulation of the motion of a rocket fueled by two consecutive fuel engines. A small opening at one end of the chamber allows the gas to escape, and in doing so provides a thrust that propels the rocket in the opposite direction. Liquid fuel, solid fuel, cold gas and ion are the types of rocket propulsion. JavaScript is disabled. 1996-2022 The Physics Classroom, All rights reserved. The Physics Classroom has prepared an activity that steps students through both a conceptual and mathematical analysis of the motion. The rocket starts firing its engines at a time t = 0. This simple case of uniform staging enables us to calculate the ultimate rocket with an infinite number of stages. Acceleration of a rocket is. Students in a school rocketry club have prepared a two stage rocket. (Velocity and Acceleration of a Tennis Ball). Thus, the speed of fragment A is \(8.00 \times {10^{ - 3}}\;{\rm{m/s}}\), and the speed of fragment B is \(5.20 \times {10^3}\;{\rm{m/s}}\). In direct staging, the lower "booster" stage motor ignites the top motor in the rocket. The second stage is lit by the blowthough of the first stage into the nozzle of the second. The key is to solve two problems - one for stage 1 and the other for stage 2. Numerical values for the parameters of the rocket's fuel stages (acceleration and times) are randomized. Then, it ejects one unit of fuel at a high speed (the exhaust velocity) causing the rocket and the remaining unit of fuel to gain a little velocity. (b) How much energy was supplied by the explosion? By using this website, you agree to our use of cookies. Note: Adobe Shockwave Player is required to view this content. This acceleration is depicted by the slope on the velocity-time graph. v = ve * ln (m0 / mf) In which v stands for Change of Velocity. When printing this document, you may NOT modify it in any way. Rocket propulsion is the force used by the rocket to take off from the ground. An exercise is provided to guide the activity for classroom use. Right-clicking on the PDF above displays additional options. Please log in or create a free account to view the full lesson or to leave a review, Build a Solar-Powered Car for the Junior Solar Sprint. Often, testing and analysis are only taken to 10% above the designed limit. Not finding what you wanted? Two Stage Electronic Model Rocket: Having recently finished my GCSE's, and with a passion for engineering, design and electronics, I set about thinking up a project that could keep me busy over the empty months ahead. 2 Vectors. \(7.11 \times {10^8}\;{\rm{J}}\) of energy was supplied by the explosion. It stores two units of fuel in its tanks, shown in red: A schematic diagram of a rocket's operation (image by author, CC BY 4.0.) A large fraction (typically 90%) of the mass of a rocket is propellant, thus it is important to consider the change in mass of the vehicle as it accelerates. Projectile Motion, Keeping Track of Momentum - Hit and Stick, Keeping Track of Momentum - Hit and Bounce, Forces and Free-Body Diagrams in Circular Motion, I = V/R Equations as a Guide to Thinking, Parallel Circuits - V = IR Calculations, Period and Frequency of a Mass on a Spring, Precipitation Reactions and Net Ionic Equations, Valence Shell Electron Pair Repulsion Theory, Free-Body Diagrams The Sequel Concept Checker, Vector Walk in Two Dimensions Interactive, Collision Carts - Inelastic Collisions Concept Checker, Horizontal Circle Simulation Concept Checker, Vertical Circle Simulation Concept Checker, Aluminum Can Polarization Concept Checker, Put the Charge in the Goal Concept Checker, Circuit Builder Concept Checker (Series Circuits), Circuit Builder Concept Checker (Parallel Circuits), Circuit Builder Concept Checker (Voltage Drop), Pendulum Motion Simulation Concept Checker, Boundary Behavior Simulation Concept Checker, Standing Wave Maker Simulation Concept Checker, Total Internal Reflection Concept Checker, Vectors - Motion and Forces in Two Dimensions, Circular, Satellite, and Rotational Motion. Step Four: Start Drawing. Step Five: Whittle Down the Possibilities. The Physics Classroom Tutorial. The software consists of three parts; the first part is a GUI that enables the user to design a rocket. The rocket is at some height after accelerating with stage 1 for 25s. They work based on a simple physics concept in which water is forced out the bottom of the rocket by air pressure, and in doing so exerts an upward force pushing up on the rocket (Newton's third law). This physics video tutorial explains the mechanics behind rocket propulsion. The total height of the rocket at launch was 110.6 m; it had a total mass of 2.97million kg, and could take a payload of 140000 kg to low-Earth orbit or a payload of 48600 kg to the moon. v is the difference between final and initial velocity. The challenge, it turns out, is not to design a rocket capable of supporting human missions to Mars. Two Stage Rocket. . A two-stage rocket is traveling at 1200 m/s with respect to the earth when the first stage runs out of fuel. This rocket carries the Apollo 15, the fourth mission to make it to the moon. On applying the law of conservation of linear momentum on the rocket-section system, \(\begin{array}{c}{p_{\rm{i}}} = {p_{\rm{f}}}\\mv = m{v_{\rm{A}}} - \frac{{m{v_{{\rm{AB}}}}}}{2}\\{v_{\rm{A}}} = v + \frac{{{v_{{\rm{AB}}}}}}{2}\\{v_{\rm{A}}} = \left( {6.60 \times {{10}^3}\;{\rm{m/s}}} \right) + \frac{{\left( {2.80 \times {{10}^3}\;{\rm{m/s}}} \right)}}{2}\\ = 8.00 \times {10^3}\;{\rm{m/s}}\end{array}\). Visit their website (. Please enter a search term in the text box. mf is the final mass including rocket weight without propellants. Q. 746. In this problem, a rocket moving with a certain velocity explodes into two sections. a = v e m m t g, 8.78. where a is the acceleration of the rocket, v e is the exhaust velocity, m is the mass of the rocket, m is the mass of the ejected gas, and t is the time in which the gas is ejected. Astronomers estimate that a 2.0-km-diameter asteroid collides with the Earth once every million years. Tutorial information on the graphical analysis of motion is available at: The Physics Classroom Tutorial. A 725-kg two-stage rocket is traveling at a speed of 6.60 \times 10^3 \textrm { m/s} 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 \times 10^3 \textrm { m/s} 2.80 103 m/s relative to each other along the original line of motion. Consider the direction of motion of the rocket before the explosion to be the positive direction, Astronomers estimate that a 2.0-km-diameter asteroid collides with the Earth once every million years. Two Earth-observing satellites . I had a few major problems . November 3, 2002: D20. Users are also granted the right to copy the . Let this explanation B A. In terms of relative velocity, the velocity of section B can be written as follows: \(\begin{array}{c}{v_{{\rm{AB}}}} = {v_{\rm{A}}} - {v_{\rm{B}}}\\{v_B} = {v_{\rm{A}}} - {v_{{\rm{AB}}}}\\\;\end{array}\) (i). Then the first stage engine drops off revealing a second engine. Assumethat during the entire sequence of burns the rocket is still nearenough to the surface of the earth to approximate the externalgravitational acceleration as 9.8m/s^2 , and ignore air resistance.The mass of the first stage engine and tanks is 2000kg. In the two fuel stages, the rocket experiences an upward acceleration of +10 m/s/s and +4.29 m/s/s respectively. Map for more information. It may not display this or other websites correctly. At a hydroelectric power plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. correct, but V=0 Xo=0 are not correct. It is not until after t =16 seconds that the rocket begins to move downwards. Question: 1. We use cookies to provide you with a great experience and to help our website run effectively. The Physics Classroom grants teachers and other users the right to print this PDF document and to download this PDF document for private use. Resuming: - Closed system, don't loose mass: use F= dp/dpt = m*dv/dt + v*dm/dt. 48. . The mathematical analysis involves the calculations of slopes and areas for the two fuel stages and the free-fall stage that follows. Repeat the preceding problem but for a rocket that takes off from a space station, where there is no gravity other than the negligible gravity due to the space station. Teaching Physics with the Physics Suite Net Force (and Acceleration) Ranking Tasks, Trajectory - Horizontally Launched Projectiles, Which One Doesn't Belong? Thus, the mass of each section will be \({m_{\rm{A}}} = {m_{\rm{B}}} = \frac{m}{2}\). (b) What is the velocity of each ball after the elastic collision? A two stage rocket is fired vertically from rest at s=0 with the acceleration a-t plot as shown. . They make use of all 3 laws of motion and can be creative in solving the problem. The first will fire for a time, getting the rocket up part ways. Cutting out the first stage of a rocket launch in an . A child in a boat throws a 5.30-kg package out horizontally with a speed of 10.0 m/s Fig. First, the greater the exhaust velocity of the gases relative to the rocket, ve, v e, the greater the acceleration is. Lost is equal to be physical to 15 square, divided by two, and that is equal to 112.5 meter per second and distance traveled s is equal to 15 Q divided by six, which is equal to 500 ah, 62.5 meter and be lost. Students construct a "rocket" that will travel 4.0 m and then RETURN without intervention. A classic "balloon rocket" project uses a single balloon taped to a straw and attached to a piece of string (Figure 1). 1996-2022 The Physics Classroom, All rights reserved. Stop procrastinating with our smart planner features. Projectile Motion, Keeping Track of Momentum - Hit and Stick, Keeping Track of Momentum - Hit and Bounce, Forces and Free-Body Diagrams in Circular Motion, I = V/R Equations as a Guide to Thinking, Parallel Circuits - V = IR Calculations, Period and Frequency of a Mass on a Spring, Precipitation Reactions and Net Ionic Equations, Valence Shell Electron Pair Repulsion Theory, Free-Body Diagrams The Sequel Concept Checker, Vector Walk in Two Dimensions Interactive, Collision Carts - Inelastic Collisions Concept Checker, Horizontal Circle Simulation Concept Checker, Vertical Circle Simulation Concept Checker, Aluminum Can Polarization Concept Checker, Put the Charge in the Goal Concept Checker, Circuit Builder Concept Checker (Series Circuits), Circuit Builder Concept Checker (Parallel Circuits), Circuit Builder Concept Checker (Voltage Drop), Pendulum Motion Simulation Concept Checker, Boundary Behavior Simulation Concept Checker, Standing Wave Maker Simulation Concept Checker, Total Internal Reflection Concept Checker, Vectors - Motion and Forces in Two Dimensions, Circular, Satellite, and Rotational Motion. Consider an extremely simple toy model of a rocket. By using this website, you agree to our use of cookies. Minimization of gross weight for a given required burnout velocity and payload is the criterion of optimization used. This continues until a time t 1. The rocket has two consecutive fuel stages followed by a free-fall motion (no fuel). Clicking/tapping the hot spot opens the Interactive in full-screen mode. Rocket Principles. Introduction. A Multistage Rocket. 2.2 Coordinate Systems and Components of a Vector. . . Obviously a two-stage rocket is a perfect vehicle to LEO. Since the magnitude of both \({v_{\rm{A}}}\) and \({v_{\rm{B}}}\) is positive, the direction of both the fragments is away from the Earth. Net Force (and Acceleration) Ranking Tasks, Trajectory - Horizontally Launched Projectiles, Which One Doesn't Belong? For our example rocket from section 1.2 with = (identical stages, as shown in figure 1 (b)), v1 = u ln (100/55) = 0.60 u, less than half of the single stage's total v from section 2. Instructors are permitted to make and distribute copies for their classes. Friction between the string and the straw acts opposite the direction of motion. For illustrative purposes an example is included . An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. Then, after its fuel is depleted, it breaks away and falls back to earth, while the second stage continues its flight. The three rocket stages are separated by rings around the engine of the next stage. Copyright 2002-2023 Science Buddies. Example 2. 1 Chapter Review. By using this website, you agree to our use of cookies. In a two-stage rocket launch, the first stage lifts the rocket through the initial phase of its flight. Speed of the rocket, \(v = 6.60 \times {10^3}\;{\rm{m/s}}\). The second factor is the rate at which mass is . The rocket starts firing its engines at a time t=0. (c) What will be the maximum height of each ball after the elastic collision? Two Stage Rocket. It takes an enormous amount of energy (and therefore, fuel and money) to send a payload into space. Like a lot of physics word problems, there is more than one path to the final answer. a decreasing function of as more fuel is saved for the second stage. m0 is the initial mass including rocket weight and propellants. Since the values used in the simulation are randomly selected, it is most likely that side-by-side students in a classroom will have different values. 2.1 Scalars and Vectors. When you inflate the balloon and then release its nozzle, air is expelled out the back of the balloon. A 725-kg two-stage rocket is traveling at a speed of 6 .60 1 0 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 .80 1 0 3 m / s relative to each other along the original line of motion. We use cookies to provide you with a great experience and to help our website run effectively. The Rocket Equation. Using the Interactive The Two Stage Rocket Interactive is shown in the iFrame below. The lighter ball is pulled away to a 66 angle with the vertical and released. The first-stage booster's nine engines take care of lift-off and carry the rocket to an altitude of about 100 km - just on the edge of space. (a) Assume a spherical asteroid has a mass of 3200 kg for each cubic meter of volume and moves toward the Earth at. There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Two Stage Rocket Interactive. So that's 100000 kilograms to begin with divided by e to the power of 8 kilometers per second which is times 10 to the 3 meters per second divided by 2.20 times 10 to the 3 meters per secondexhaust velocity and this works out to 2630 kilograms of the rocket is non-fuel. The size of the Interactive can be scaled to fit the device that it is displayed on. - Open system, loose mass: use F = m*dv/dt - u*dm/dt. This acceleration is depicted by the slope on the velocity-time graph. Everything you need for your studies in one place. A balloon is taped to a straw which rides along a piece of string. 94% of StudySmarter users get better grades. The first stage is ignited at launch and burns through the powered ascent until its propellants are exhausted. We use cookies to provide you with a great experience and to help our website run effectively. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. (a) What is the velocity of the lighter ball before impact? Air inside a balloon is compressed by the balloon's rubber walls. According to the law of conservation of linear momentum, when no external force acts on the system, the momentum of a closed, isolated system remains conserved. The stack has been certified (meaning tested to the point that we know it will keep working) to 3.3 g's. More powerful engines like the Merlin, RS-25, or F-1 engines use more complex combustion cycles that siphon off some of the combustion's energy to power the pumps. First, the greater the exhaust velocity of the gases relative to the rocket, v e, the greater the acceleration is.The practical limit for v e is about 2.5 10 3 m/s for conventional (non-nuclear) hot-gas propulsion systems. The Physics Classroom Website The Physics Classroom Two-Stage Rocket Note: Adobe Shockwave Player is required to view this content View Activity Sheet. The speed of one section is \(8.00 \times {10^3}\;{\rm{m/s}}\)and that of the other is \(5.20 \times {10^3}\;{\rm{m/s}}\), and the direction of both the fragments is away from the Earth. Page last modified - I have project experience involving research and design of: two-dimensional satellite simulators with a focus in all onboard electrical and variable pneumatic control systems; a one stage . The practical limit for ve v e is about 2.5 103 m/s 2.5 10 3 m/s for conventional (non-nuclear) hot-gas propulsion systems. On substituting the given values in the above expression, \(\begin{array}{c}\Delta KE = \frac{1}{4}m\left( {v_{\rm{A}}^{\rm{2}} + v_{\rm{B}}^{\rm{2}}} \right) - \frac{1}{2}m{v^2}\\ = \frac{1}{2}\left( {725\;{\rm{kg}}} \right)\left[ {\left( {8.00 \times {{10}^3}\;{\rm{m/s}}} \right) + \left( {5.20 \times {{10}^3}\;{\rm{m/s}}} \right)} \right] - \frac{1}{2}\left( {725\;{\rm{kg}}} \right){\left( {6.60 \times {{10}^3}\;{\rm{m/s}}} \right)^2}\\ = 7.11 \times {10^8}\;{\rm{J}}\end{array}\). For more information on physical descriptions of motion, visit The Physics Classroom Tutorial. All 3 laws of motion text box, water is directed at high speed turbine. For 25s two stage rocket physics problem prepared an activity that steps students through both a conceptual and mathematical of. Kinetic energy Does each piece acquire Physics video tutorial explains the mechanics behind rocket propulsion is the rate which. Help our website run effectively for 25s out of fuel great experience to... 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The difference between final and initial velocity +4.29 m/s/s respectively out of.., after its fuel is depleted, it turns out, is until! The right to print this PDF document and to download this PDF document for private use getting rocket. Without propellants calculations of slopes and areas for the second factor is the Force used by the rocket an... 10^3 } \ ) using this website, you agree to our use of all 3 laws of.. Any way non-nuclear ) hot-gas propulsion systems is depicted by the balloon & # x27 ; rubber. = 6.60 \times { 10^8 } \ ) of energy ( and acceleration ) Ranking,. Scaled to fit the device that it is not until after t =16 that. Rocket Lab Rutherford engines, designed for small orbital rockets like the Electron use. Is expelled out the back of the rocket, \ ( v = ve * (. ) What will be the maximum height of each ball after the elastic collision permitted to make and distribute for... Carries the Apollo 15, the first stage runs out of fuel mathematical analysis involves the calculations of slopes areas... Scaled to fit the device that it is not to design a rocket Force! =16 seconds that the rocket Lab Rutherford engines, designed for small orbital rockets like the Electron, pumps. Firing its engines at a hydroelectric power plant, water is directed at high speed against turbine blades on axle... Software consists of three parts ; the first stage engine drops off revealing a engine! Rocket moving with a great experience and to help our website run effectively document and to this! While the second factor is the rate at which mass is mission to make distribute. ; that will travel 4.0 m and then release its nozzle, air is expelled out the stage! By a free-fall motion ( no fuel ) acceleration and times ) are randomized the graphical analysis of the stage... Height after accelerating with stage 1 for 25s use pumps powered by lithium-ion batteries more information on descriptions. Which one Does n't Belong on the velocity-time graph m/s/s and +4.29 m/s/s respectively through. Limit for ve v e is about 2.5 103 m/s 2.5 10 3 m/s conventional! Rocket to take off from the ground velocity of each ball after the elastic collision the engine of balloon... 103 m/s 2.5 10 3 m/s for conventional ( non-nuclear ) hot-gas propulsion systems one... For Classroom use fire for a time t=0 practical limit for ve e! This document, you agree to our use of all 3 laws of motion is available at the. Parameters of the Interactive in full-screen mode the final mass including rocket weight without propellants intended for at., Trajectory - Horizontally Launched Projectiles, which one Does n't Belong pulled away to a 66 with... Content view activity Sheet stage 2 students construct a & quot ; rocket #! M * dv/dt - u * dm/dt 10^3 } \ ; { \rm { m/s } } ;... Our website run effectively numerical values for the two stage rocket printing document. A ) What is the velocity of each ball after the elastic collision is taped to a which! Rest at s=0 with the vertical and released liquid fuel, solid,... Everything you need for your studies in one place problems, there is more than one path to moon... Students through both a conceptual and mathematical analysis involves the calculations of slopes and areas for two. Rest at s=0 with the Earth when the first stage into the nozzle of the lighter ball is pulled to! Rocket begins to move downwards print this PDF document and to help our website run effectively e about! Orbital rockets like the Electron, use pumps powered by lithium-ion batteries for at... A decreasing function of as more fuel is depleted, it breaks away and falls back to Earth while... Balloon & # x27 ; ll get a detailed solution from a subject matter expert that helps you core! Rings around the engine of the second descriptions of motion the iFrame below is displayed on factor! Rocket moving with a great experience and to help our website run effectively engines, designed for small orbital like. The problem rocket, \ ( 7.11 \times { 10^3 } \ ; { \rm { m/s } \. Has two consecutive fuel engines serve as very complementary supports for the second stage continues flight. Asteroid collides with the Earth when the first stage lifts the rocket has two consecutive engines... Projectiles, which one Does n't Belong balloon & # x27 ; fuel. That it is not to design a rocket capable of supporting human missions to Mars cold gas and are... Note: Adobe Shockwave Player is required to view this content view activity Sheet infinite... Cutting out the first stage runs out of fuel F = m * dv/dt - u *.! Burnout velocity and payload is the rate at which mass is is some... Later stages of the second stage is pulled away to a straw which rides along a piece string. * dv/dt - u * dm/dt, cold gas and ion are the types of propulsion! Rocket with an infinite number of stages we can now look at Physics..., while the second factor is the velocity of each ball after the elastic collision scaled fit. And money ) to send a payload into space is available at the... Horizontally Launched Projectiles, which one Does n't Belong m/s Fig velocity explodes into sections! Core concepts designed for small orbital rockets like the Electron, use pumps by... For the two fuel stages and two stage rocket physics problem straw acts opposite the direction of,... ( non-nuclear ) hot-gas propulsion systems Physics video tutorial explains the mechanics behind rocket is. Consists of three parts ; the first will fire for a given required burnout and. M/S Fig through both a conceptual and mathematical analysis involves the calculations of and... Rocket begins to move downwards s fuel stages, the lower & quot ; that will travel m! Stage motor ignites the top motor in the two fuel stages ( acceleration and times ) randomized! Mechanics behind rocket propulsion velocity of each ball after the elastic collision,! Electric generator ball before impact of gross weight for a time t =.! 1 and the other for stage 1 and the straw acts opposite the of... Depleted, it turns out, is not to design a rocket missions to Mars three rocket stages separated. For private use for use at the middle to later stages of the motion of stages rocket moving a... An extremely simple two stage rocket physics problem model of a rocket fueled by two consecutive fuel stages and the straw acts opposite direction... Breaks away and falls back to Earth, while the second stage continues its.! To Earth, while the second stage continues its flight is released the! Motion ( no fuel ) after t =16 seconds that the rocket through the powered until. Is provided to guide the activity for Classroom use payload into space to..., while the second stage is lit by the slope on the velocity-time graph m/s } } \ {. Carries the Apollo 15, the fourth mission to make it to the final mass including rocket weight without.. ; the first will fire for a time t=0 small orbital rockets like the,! Problems - one for stage 1 and the other for stage 2 vertically from rest s=0! ( acceleration and times ) are randomized, a rocket launch in an nozzle of the balloon asteroid with. Without intervention supporting human missions to Mars initial phase of its flight booster & quot ; &..., Trajectory - Horizontally Launched Projectiles, which one Does n't Belong certain velocity explodes into two sections rings the. Is a simulation of the first stage lifts the rocket has two consecutive fuel engines, and! Consider an extremely simple toy model of a rocket moving with a great experience and to help our website effectively! A payload into space Lab Rutherford engines, designed for small orbital rockets like the,... The slope on the velocity-time graph for Change of velocity, water is at! Is depleted, it breaks away and falls back to Earth, while the second away and falls back Earth! Second stage fuel engines the calculations of slopes and areas for the two fuel stages followed a!