Determine the altitude reached by the spacecraft of Prob. 14.95 when all the fuel of its launching rocket has been consumed.
14.95 A 540-kg spacecraft is mounted on top of a rocket with a mass of 19 Mg, including 17.8 Mg of fuel. Knowing that the fuel is consumed at a rate of 225 kg/s and ejected with a relative velocity of 3600 m/s, determine the maximum speed imparted to the spacecraft if the rocket is fired vertically from the ground.
Fig. P14.95
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
<LCPO> VECTOR MECH,STAT+DYNAMICS
Additional Engineering Textbook Solutions
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
Applied Statics and Strength of Materials (6th Edition)
Engineering Mechanics: Statics
Engineering Mechanics: Dynamics (14th Edition)
Fundamentals of Aerodynamics
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
- The rocket engines of a spacecraft are fired to increase its velocity by 450 ft/s. Knowing that 1200 lb of fuel is ejected at a relative velocity of 5400 ft/s, determine the weight of the spacecraft after the firing.arrow_forwardA rocket weighs 2600 lb, including 2200 lb of fuel, which is consumed at the rate of 25 lb/s and ejected with a relative velocity of 13,000 ft/s. Knowing that the rocket is fired vertically from the ground, determine (a) its acceleration as it is fired, (b) its acceleration as the last particle of fuel is being consumed, (c) the altitude at which all the fuel has been consumed, (d) the velocity of the rocket at that time.arrow_forwardThe weight of a spacecraft, including fuel, is 11,600 lb when the rocket engines are fired to increase its velocity by 360 ft/s. Knowing that 1000 lb of fuel is consumed, determine the relative velocity of the fuel ejected.arrow_forward
- A railroad car with length L and mass m0 when empty is moving freely on a horizontal track while being loaded with sand from a stationary chute at a rate dm/dt =q . Knowing that the car was approaching the chute at a speed v0 , determine (a) the mass of the car and its load after the car has cleared the chute, (b) the speed of the car at that time.arrow_forwardPROBLEM 12.6 A 0.1-kg model rocket is launched vertically from rest at time t=0 with a constant thrust of 10 N for one second and no thrust for t > 1 s. Neglecting air resistance and the decrease in mass of the rocket, determine (a) the maximum height h reached by the rocket, (b) the time required to reach this maximum height. h = 460 m t = 10.19 sarrow_forwardA spacecraft is moving in gravity-free space along a straight path when its pilot decides to accelerate forward. He turns on the thrusters, and burned fuel is ejected at a constant rate of 2.0 × 102 kg/s, at a speed (relative to the rocket) of 2.5 × 10² m/s. The initial mass of the spacecraft and its unburned fuel is 2.0 × 104 kg, and the thrusters are on for 30 s. a. What is the thrust (the force applied to the rocket by the ejected fuel) on the spacecraft? b. What is the spacecraft's acceleration as a function of time? c. What are the spacecraft's accelerations at t = 0, 15, 30, and 35 s?arrow_forward
- It takes 15 s to raise a 1200-kg car and the supporting 300-kg hydraulic car-lift platform to a height of 2.8 m. Determine (a) the average output power delivered by the hydraulic pump to lift the system, (b) the average electric power required, knowing that the overall conversion efficiency from electric to mechanical power for the system is 82 percent.arrow_forwardA toy car is propelled by water that squirts from an internal tank. The weight of the empty car is 0.4 lb and it holds 2 lb of water. Knowing the top speed of the car is 8 ft/s, determine the relative velocity of the water that is being ejected.arrow_forward14.49 Two small spheres A and B, with masses of 2.5 kg and 1 kg, re- spectively are connected by a rigid rod of negligible mass. The two spheres are resting on a horizontal, frictionless surface when A is suddenly given the velocity vo = (3.5 m/s)i. Determine (a) the linear momentum of the system and its angular momentum about its mass center G, (b) the velocities of A and B after the rod AB has rotated through 180°. B 210 mmarrow_forward
- A spacecraft is placed into a polar orbit about the planet Mars at an altitude of 380 km. Knowing that the mean density of Mars is 3.94 Mg/m^3 and that the radius of Mars is 3397 km, determine the time t required for the spacecraft to complete one full revolution about Mars and the velocity with which the the spacecraft describes its orbit.arrow_forwardA 1.4-kg model rocket is launched vertically from rest with a constant thrust of 25 N until the rocket reaches an altitude of 15 m and the thrust ends. Neglecting air resistance, determine (a) the speed of the rocket when the thrust ends, (b) the maximum height reached by the rocket, (c) the speed of the rocket when it returns to the ground.arrow_forwardA 1-lb stone is dropped down the “bottomless pit” at Carlsbad Caverns and strikes the ground with a speed of 95 ft/s. Neglecting air resistance, (a) determine the kinetic energy of the stone as it strikes the ground and the height h from which it was dropped. (b) Solve part aassuming that the same stone is dropped down a hole on the moon. (Acceleration of gravity on the moon = 5.31 ft/s2).arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY