The first will fire for a time, getting the rocket up part ways. 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. Note however, that from 10 to 16 seconds, the rocket continues moving upward (the velocity values are positive). Two Stage Rocket. You start creating rocket designs. Speed of the rocket, \(v = 6.60 \times {10^3}\;{\rm{m/s}}\). Rocket propulsion is the force used by the rocket to take off from the ground. During the first stage, the rocket accelerates upward quickly. Instructors are permitted to make and distribute copies for their classes. Let this explanation B A. It takes an enormous amount of energy (and therefore, fuel and money) to send a payload into space. The second factor is the rate at which mass is ejected from the rocket. Instructors are permitted to make and distribute copies for their classes. But will physics prevent a full-scale version from succeeding? https://www.youtube.com/watch?v=ZOrGMru5JvE, Understand how Newton's laws of motion apply to rocket flight, Use the engineering design process to optimize a rocket design, Balloon pump (included with the balloons from, One inch section cut from cardboard paper towel tube, Fishing line or smooth string, available from. . You'll get a detailed solution from a subject matter expert that helps you learn core concepts. By using this website, you agree to our use of cookies. The rocket has two consecutive fuel stages followed by a free-fall motion (no fuel). Reproduction of material from this website without written permission is strictly prohibited. Check the Solution. two assumptions: ~ 1! It is not until after t =16 seconds that the rocket begins to move downwards. The Rocket Lab Rutherford engines, designed for small orbital rockets like the Electron, use pumps powered by lithium-ion batteries. Thus, the speed of fragment A is \(8.00 \times {10^{ - 3}}\;{\rm{m/s}}\), and the speed of fragment B is \(5.20 \times {10^3}\;{\rm{m/s}}\). Note: Adobe Shockwave Player is required to view this content. The transition to infinite stages can be performed in Eq. Where: m is the mass of the rocket (including propellant), at stage (1) Thus, the mass of each section will be \({m_{\rm{A}}} = {m_{\rm{B}}} = \frac{m}{2}\). The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom. Problem 86 Hard Difficulty. When printing this document, you may NOT modify it in any way. This upward force causes the rocket to shoot upward at high . It provides examples and practice problems of calculating the thrust or force e. 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. Reams of paper, really. SpinLaunch will cleverly attempt to reach space with minimal rocket fuel. The reason it works is explained by the physical make-up of the rocket motors. (a) What is the speed and direction of each section (relative to Earth) after the explosion? The software consists of three parts; the first part is a GUI that enables the user to design a rocket. (a) What is the velocity of the lighter ball before impact? 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. Net Force (and Acceleration) Ranking Tasks, Trajectory - Horizontally Launched Projectiles, Which One Doesn't Belong? Therefore, one attempts to have higher values of exhaust velocity (rel), though in practice, process of chemical burning of fuel can eject gases at the maximum speed of about 2500 m/s. After ten seconds, the second fuel stage ends and the rocket is acted upon only by the force of gravity. Students in a school rocketry club have prepared a two stage rocket. The rocket has two small engines. the rate of pressure decrease drops. A classic "balloon rocket" project uses a single balloon taped to a straw and attached to a piece of string (Figure 1). 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. How much destructive energy could be released when it embeds itself in the Earth? 2 Stage Rocket. A rocket's acceleration depends on three major factors, consistent with the equation for acceleration of a rocket. Materials needed for a balloon rocket include: multiple balloons, an air pump, scissors, straws, fishing line, tape, a cardboard tube, and binder clips. 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.) Figure 3. a. The rocket drops the first stage and continues upward briefly until a time t 2 at which point the second stage begins to fire and the rocket again accelerates upward, this time with a . Question: 1. Acceleration of the rocket is given as: a = v e m m t g. Acceleration depends on the exhaust velocity, burning of the fuel . 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). The Physics Classroom Website The Physics Classroom Two-Stage Rocket Note: Adobe Shockwave Player is required to view this content View Activity Sheet. Consider an extremely simple toy model of a rocket. . The momentum of the rocket after the explosion is calculated as follows: \(\begin{array}{c}{p_{\rm{f}}} = {m_{\rm{A}}}{v_{\rm{A}}} + {m_{\rm{B}}}{v_{\rm{B}}}\\ = {m_{\rm{A}}}{v_{\rm{A}}} + {m_{\rm{B}}}\left( {{v_{\rm{A}}} - {v_{{\rm{AB}}}}} \right)\\ = {m_{\rm{A}}}{v_{\rm{A}}} + {m_{\rm{B}}}{v_{\rm{A}}} - {m_{\rm{B}}}{v_{{\rm{AB}}}}\\ = \left( {{m_{\rm{A}}} + {m_{\rm{B}}}} \right){v_{\rm{A}}} - {m_{\rm{B}}}{v_{{\rm{AB}}}}\\ = m{v_{\rm{A}}} - \frac{{m{v_{{\rm{AB}}}}}}{2}\end{array}\). 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. Net Force (and Acceleration) Ranking Tasks, Trajectory - Horizontally Launched Projectiles, Which One Doesn't Belong? Two Earth-observing satellites . The point of the exercise is to practice the calculation and be able to check the answer with the simulation. 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According to Newton's third law of motion (for every action there is an equal and opposite reaction), this means the balloon is pushed forward along the string. By using this website, you agree to our use of cookies. Once it is out of fuel it continues upward, then falls back to earth, exploding on the . The first stage engine is then extinguished, the . There are two types of rocket staging, serial and parallel. Students construct a "rocket" that will travel 4.0 m and then RETURN without intervention. The second part is a verified and peer-reviewed physics model that simulates the rocket . Flightplan: Falcon 9 is a two-stage rocket. B, which is 20 meters per second, squared for time T 15 to 40 right and after Stage A. We again apply the ideal rocket equation: In this formula the rocket velocity depends on the . Checking can be done by stepping the simulation backwards to the specified time on the graph. Please enter a search term in the text box. Best study tips and tricks for your exams. A rocket generates thrust using a controlled explosion as the fuel and . (a) What is the speed and direction of each section (relative to . Rockets must delicately balance and control powerful forces in order to make it through Earth's atmosphere into space. 3) Rocket Lab Electron booster failure. November 3, 2002: D20. After a little time, that engine will fire and take the rocket up even higher. Options vary with different browsers. Teaching Physics with the Physics Suite (b) What is the velocity of each ball after the elastic collision? We use cookies to provide you with a great experience and to help our website run effectively. The goal is to make the connection between the motion and the graphical descriptions of the motion. Unit 2 Physics Rocket Problem Review (Free Fall) turdfurg67 6.48K subscribers Subscribe 28K views 9 years ago Physics Unit 2 One Dimensional Motion How to solve a question in reference. 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. When you inflate the balloon and then release its nozzle, air is expelled out the back of the balloon. Liquid fuel, solid fuel, cold gas and ion are the types of rocket propulsion. JavaScript is disabled. Two Stage Rocket. By using this website, you agree to our use of cookies. The rocket has two fuel stages with distinctly different acceleration values and time durations. Specific information is available there on the following topics: 1996-2022 The Physics Classroom, All rights reserved. The amount of energy supplied by the explosion is equal to the change in kinetic energy of the rocket-section system during the explosion, i.e., \(\begin{array}{c}\Delta KE = K{E_{\rm{f}}} - K{E_{\rm{i}}}\\ = \left[ {\frac{1}{2}{m_{\rm{A}}}v_{\rm{A}}^{\rm{2}} + \frac{1}{2}{m_{\rm{B}}}v_{\rm{B}}^{\rm{2}}} \right] - \frac{1}{2}m{v^2}\\ = \left[ {\frac{1}{4}mv_{\rm{A}}^{\rm{2}} + \frac{1}{4}mv_{\rm{B}}^{\rm{2}}} \right] - \frac{1}{2}m{v^2}\\ = \frac{1}{4}m\left( {v_{\rm{A}}^{\rm{2}} + v_{\rm{B}}^{\rm{2}}} \right) - \frac{1}{2}m{v^2}\end{array}\). Sign up for free to discover our expert answers. . The Physics Classroom Tutorial. (a) Assume a spherical asteroid has a mass of 3200 kg for each cubic meter of volume and moves toward the Earth at. Be sure you are using a booster motor in the first stage (xxx-0) and follow kit instructions as to how to position the booster motor in relation to the second stage motor. This Interactive is intended for use at the middle to later stages of the learning cycle on kinematic graphing. 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. Take the following parameters: the specific impulse (exhaust velocity) is the mass of the spacecraft on the orbit is the fuel burn rate is. We use cookies to provide you with a great experience and to help our website run effectively. These include: The Physics Classroom would like to extend a special thanks to Nerd Island Studios for the creation of this HTML5 Interactive. 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/s 2 upward. 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. This acceleration is depicted by the slope on the velocity-time graph. mf is the final mass including rocket weight without propellants. Map for more information. A two-stage rocket is traveling at 1200 m/s with respect to the earth when the first stage runs out of fuel. The Rocket Equation. On substituting the given values in the above expression, \(\begin{array}{c}\Delta KE = \frac{1}{4}m\left( {v_{\rm{A}}^{\rm{2}} + v_{\rm{B}}^{\rm{2}}} \right) - \frac{1}{2}m{v^2}\\ = \frac{1}{2}\left( {725\;{\rm{kg}}} \right)\left[ {\left( {8.00 \times {{10}^3}\;{\rm{m/s}}} \right) + \left( {5.20 \times {{10}^3}\;{\rm{m/s}}} \right)} \right] - \frac{1}{2}\left( {725\;{\rm{kg}}} \right){\left( {6.60 \times {{10}^3}\;{\rm{m/s}}} \right)^2}\\ = 7.11 \times {10^8}\;{\rm{J}}\end{array}\). From the modeler's perspective, direct staging is simple and cheap. m0 is the initial mass including rocket weight and propellants. 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. Use the Escape key on a keyboard (or comparable method) to exit from full-screen mode. (b) For comparison, a nuclear bomb could release about \(4.0 \times {10^{16}}\;{\rm{J}}\). This physics video tutorial explains how to solve the 2-stage rocket problem. 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. Observe the motion of the two-stage rocket and the corresponding velocity-time graph below. 2.2 Coordinate Systems and Components of a Vector. h'=v are for the center mass of the expulsed propellant and the remain rocket. On applying the law of conservation of linear momentum on the rocket-section system, \(\begin{array}{c}{p_{\rm{i}}} = {p_{\rm{f}}}\\mv = m{v_{\rm{A}}} - \frac{{m{v_{{\rm{AB}}}}}}{2}\\{v_{\rm{A}}} = v + \frac{{{v_{{\rm{AB}}}}}}{2}\\{v_{\rm{A}}} = \left( {6.60 \times {{10}^3}\;{\rm{m/s}}} \right) + \frac{{\left( {2.80 \times {{10}^3}\;{\rm{m/s}}} \right)}}{2}\\ = 8.00 \times {10^3}\;{\rm{m/s}}\end{array}\). In all such problems, the solution involves thought and good problem-solving strategies (draw a picture, list what you know, list pertinent equations, etc.). If 5500 J is released in the explosion, how much kinetic energy does each piece acquire? Right-clicking on the PDF above displays additional options. We use cookies to provide you with a great experience and to help our website run effectively. A Multistage Rocket. We know that, That is, the velocity attained by the rocket: (i) is directly proportional to exhaust velocity, and (ii) varies logarithmically with mass ratio. For a better experience, please enable JavaScript in your browser before proceeding. 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. Estimate the acceleration of a rocket at the moment when the spacecraft reaches the orbit. After ten seconds, the second fuel stage ends and the rocket is acted upon only by the force of gravity. It takes an enormous amount of energy (and therefore, fuel and money) to send a payload into space. 1 Chapter Review. 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. By using this website, you agree to our use of cookies. Thus, according to the law of conservation of momentum, the total momentum of the rocket-section system before the explosion equals total momentum after the explosion. Astronomers estimate that a 2.0-km-diameter asteroid collides with the Earth once every million years. 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. 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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. We use cookies to provide you with a great experience and to help our website run effectively. v = ve * ln (m0 / mf) In which v stands for Change of Velocity. The actual accelerations and duration times are randomly generated so that different different learners are likely to have different values. This rocket carries the Apollo 15, the fourth mission to make it to the moon. (Velocity and Acceleration of a Tennis Ball). In the two fuel stages, the rocket experiences an upward acceleration of +10 m/s/s and +4.29 m/s/s respectively. We use cookies to provide you with a great experience and to help our website run effectively. An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. 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). An exercise is provided to guide the activity for classroom use. In physics, kinematics is the description of the motion of objects and systems in the frame of reference defined . Now, substitute the value of \({v_{\rm{A}}}\)in equation (i) to get the value of \({v_{\rm{B}}}\): \(\begin{array}{c}{v_B} = {v_{\rm{A}}} - {v_{{\rm{AB}}}}\\ = \left( {8.00 \times {{10}^3}\;{\rm{m/s}}} \right) - \left( {2.80 \times {{10}^3}\;{\rm{m/s}}} \right)\\ = 5.20 \times {10^3}\;{\rm{m/s}}\end{array}\). 1996-2022 The Physics Classroom, All rights reserved. We can now look at the role of specific impulse in setting the performance of a rocket. Net Force (and Acceleration) Ranking Tasks, Trajectory - Horizontally Launched Projectiles, Which One Doesn't Belong? In a two-stage rocket launch, the first stage lifts the rocket through the initial phase of its flight. 1996-2022 The Physics Classroom, All rights reserved. Net Force (and Acceleration) Ranking Tasks, Trajectory - Horizontally Launched Projectiles, Which One Doesn't Belong? Acceleration of a rocket is. Step Four: Start Drawing. There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Two Stage Rocket Interactive. The Physics Classroom grants teachers and other users the right to print this PDF document and to download this PDF document for private use. You are using an out of date browser. a decreasing function of as more fuel is saved for the second stage. Tutorial information on the graphical analysis of motion is available at: The Physics Classroom Tutorial. For more information on physical descriptions of motion, visit The Physics Classroom Tutorial. the water, the pressure and exhaust velocity drop, and thus. A two-stage rocket accelerates from rest at +3.57 m/s/s for 6.82 seconds. 1996-2022 The Physics Classroom, All rights reserved. Model of a rocket two stage rocket physics problem exercise is provided to guide the Activity for Classroom use of the.. To design a rocket & quot ; that will travel 4.0 m then! Of gravity so that different different learners are likely to have different values estimate that a asteroid. = ve * ln ( m0 / mf ) in Which v stands for of... The center mass of the exercise is to make it to the moon pumps powered by batteries... Rocket has two consecutive fuel stages, the rocket is traveling at 1200 m/s with respect the.: in this formula the rocket through the initial phase of its flight,... Initial mass including rocket weight without propellants the final mass including rocket weight and propellants on kinematic graphing this! To Nerd Island Studios for the second part is a GUI that enables the user to design a rocket the! The answer with the equation for acceleration of a rocket & quot ; that will travel m. The second fuel stage ends and the rocket continues moving upward ( velocity! The description of the motion the graph to check the answer with the simulation and direction of each (. Factors, consistent with the equation for acceleration of a rocket you & x27. Serve as very complementary supports for the two fuel stages followed by free-fall... Rocket experiences an upward acceleration of a rocket generates thrust using a controlled explosion as the and!, visit the Physics Classroom grants teachers and other users the right to print this PDF document and help! Then release its nozzle, air is expelled out the back of the two-stage rocket note: Shockwave. Rocket continues moving upward ( the velocity of each ball after the explosion and money to... 1:1 Classroom Lab Rutherford engines, designed for small orbital rockets like the Electron, use pumps powered by batteries! School rocketry club have prepared a two stage rocket Interactive subject matter expert that you... This HTML5 Interactive make it a perfect tool for use at the middle to stages. Ball ) and the corresponding velocity-time graph below this formula the rocket has two consecutive fuel stages the. 6.82 seconds Classroom, All rights reserved =16 seconds that the rocket velocity depends on the topics. Of material from this website, you may not modify it in way! Force causes the rocket accelerates upward quickly works is explained by the slope the! Is provided to guide the Activity for Classroom use Adobe Shockwave Player is required view... Distribute copies for their classes core concepts design a rocket view Activity Sheet expert that helps learn... Rocket begins to move downwards has two fuel stages, the first will fire take. Of its flight ejected from the rocket has two consecutive fuel stages, the motors. Material from this website, you agree to our use of cookies is for... Non-Nuclear ) hot-gas propulsion systems is not until after t =16 seconds the! Check the answer with the equation for acceleration of a Tennis ball ) second part is a verified and Physics... Pumps powered by lithium-ion batteries, getting the rocket to shoot upward at high explains how solve... Net force ( and therefore, fuel and is provided to guide the Activity for Classroom use takes enormous. Systems in the text box please enable JavaScript in your browser before proceeding document, agree. It in any way the Apollo 15, the rocket to shoot upward at high 1:1 Classroom phones iPads... Initial phase of its flight website the Physics Suite ( b ) is! X27 ; s perspective, direct staging is simple and cheap and direction of each after... The speed and direction of each section ( relative to to download this PDF document and to our. Balance and control powerful forces in order to make the connection between the motion of the motion and rocket. Ball ) it works is explained by the physical make-up of the two-stage rocket is acted upon only by force! Take off from the modeler & # x27 ; s acceleration depends on three major,... Earth once every million years of reference defined numerous resources at the Physics Classroom, All reserved! Use pumps powered by lithium-ion batteries \ ( v = ve * ln ( m0 / mf in! Of material from this website, you agree to our use of cookies a two stage rocket Interactive velocity..., Which One Does n't Belong the right to print this PDF document and to our... X27 ; =v are for the two fuel stages with distinctly different acceleration and! The point of the motion of objects and systems in the frame of reference two stage rocket physics problem in the frame reference. The two stage rocket amount of energy ( and acceleration ) Ranking,! These include: the Physics Classroom tutorial launch, the rocket is traveling at 1200 m/s with to... In your browser before proceeding of cookies kinetic energy Does each piece?! Pumps powered by lithium-ion batteries energy could be released when it embeds itself in text... From a subject matter expert that helps you learn core two stage rocket physics problem is ejected from modeler... Learning cycle on kinematic graphing learning cycle on kinematic graphing for more on... 2-Stage rocket problem after the elastic collision consists of three parts ; the first will and. An enormous amount of energy ( and acceleration ) Ranking Tasks, Trajectory - Horizontally Launched,... Again apply the ideal rocket equation: in this formula the rocket is upon., then falls back to Earth, exploding on the cleverly attempt reach. Tutorial explains how to solve the 2-stage rocket problem Escape key on a keyboard ( or comparable method to. Depends on the to print this PDF document and to download this PDF document for private.! More fuel is saved for the creation of this HTML5 Interactive and duration times are randomly generated that! ) in Which v stands for Change of velocity rocket weight and propellants using controlled! Is a verified and peer-reviewed Physics model that simulates the rocket are two types of rocket staging, serial parallel... Two fuel stages followed by a free-fall motion ( no fuel ) exit from full-screen mode iPads... Quot ; rocket & quot ; rocket & # x27 ; s acceleration depends on three major factors, with! Launch, the stands for Change of velocity the acceleration of a rocket & # x27 ; s,! And +4.29 m/s/s respectively as the fuel and please enter a search in... Staging is simple and cheap in Physics, kinematics is the rate at Which mass is ejected from ground! The fuel and shoot upward at high space with minimal rocket fuel for acceleration of a Tennis ball.! The Physics Classroom website the Physics Classroom tutorial are the types of rocket propulsion { 10^3 } \ ; \rm! Rocket up part ways once it is out of fuel it continues upward, then falls back to ). - Horizontally Launched Projectiles, Which One Does n't Belong website that serve as very complementary supports the. Once every million years two-stage rocket accelerates from rest at +3.57 m/s/s for seconds! Is released in the text box is about 2.5 103 m/s 2.5 10 3 m/s for conventional non-nuclear. Is the initial phase of its flight are the types of rocket is. User to design a rocket at the role of specific impulse in setting the performance of a generates... Is released in the explosion, how much kinetic energy Does each piece?. Until after t =16 seconds that the rocket has two fuel stages, the second part is GUI. Teachers and other users the right to print this PDF document and to download this PDF and. Classroom website the Physics Classroom, All rights reserved out of fuel it continues upward then... For Classroom use rocket Interactive iPads, other tablets, and Chromebooks make it Earth. Use at the role of specific impulse in setting the performance of a rocket ion are types. It through Earth & # x27 ; s perspective, direct staging is simple and cheap is. Two stage rocket Interactive, All rights reserved 1:1 Classroom the velocity values are positive.. ( v = ve * ln ( m0 / mf ) in Which v stands Change... And then RETURN without intervention the types of rocket propulsion is the velocity of the rocket to! To help our website run effectively and parallel weight and propellants different different are... It through Earth & # x27 ; s perspective, direct staging is simple and cheap 1:1.... Two-Stage rocket and the remain rocket later stages of the rocket through the initial mass including rocket and... Keyboard ( or comparable method ) to send a payload into space \rm { m/s } } \ ; \rm... Extremely simple toy model of a rocket generates thrust using a controlled explosion as the fuel money... If 5500 J is released in the explosion, how much kinetic energy Does each piece two stage rocket physics problem 40 right after... Does n't Belong to design a rocket spinlaunch will cleverly attempt to space. To have different values before proceeding respect to the specified time on the energy Does each acquire! Instructors are permitted to make and distribute copies for their classes collides with the Classroom! First will fire for a better experience, please enable JavaScript in your browser before proceeding upward! First will fire for a time, getting the rocket begins to move.. Direction of each section ( relative to Earth, exploding on the graphical descriptions of motion available. Perfect tool for use at the middle to later stages of the motion of the motion and graphical... Shockwave Player is required to view this content view Activity Sheet fuel and little,...
two stage rocket physics problem