Concept explainers
A 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.
The acceleration as it is fired of the rocket.
Answer to Problem 14.100P
The value of acceleration is a=92.8ft/s2
Explanation of Solution
The weight of the rocket as:
Substitute
Substitute required values, we get:
The acceleration as the last particle of fuel is consumed.
Answer to Problem 14.100P
The value of acceleration as the last particle of fuel is a=780ft/s2.
Explanation of Solution
Find the weight of the rocket the condition is fuel is consumed.
Substituting all required values, we get:
The weight of the rocket is:
Substitute all the values, we get:
The altitude at which all the fuel has been consumed.
Answer to Problem 14.100P
The value of altitude at which all the fuel has been consumed is
Explanation of Solution
Formulate the relation for final velocity of the rocket is:
Consider the relation for the altitude of the rocket:
Here
Here
So,
Substitute these values, we get:
Substitute
Find the time t by using below formula, we get:
Substitute all the values, we get:
The velocity of the rocket.
Answer to Problem 14.100P
The value of velocity at that time is V
Explanation of Solution
Substitute all the required values in equation 1, we get:
Want to see more full solutions like this?
Chapter 14 Solutions
Vector Mechanics For Engineers
- The rocket used to launch the 540-kg spacecraft of Prob. 14.95 is redesigned to include two stages A and B , each of mass 9.5 Mg, including 8.9 Mg of fuel. The fuel is again consumed at a rate of 225 kg/s and ejected with a relative velocity of 3600 m/s. Knowing that when stage A expels its last particle of fuel, its casing is released and jettisoned, determine (a) the speed of the rocket at that instant, (b) the maximum speed imparted to the spacecraft.Reference to Problem 14.95:arrow_forwardDetermine the altitude reached by the spacecraft of Prob. 14.95 when all the fuel of its launching rocket has been consumed.Reference to Problem 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.arrow_forwardAn orbiting satellite has a mass of 5000 kg and is travelling at a constant velocity of V0. To alter its orbit, an attached rocket discharges 100 kg of gases from the reaction of solid fuel at a speed of 3000 m/s relative to the satellite in a direction opposite V0. The fuel discharge rate is constant for 2 s. Determine(a) The thrust exerted on the satellite.(b) The acceleration of the satellite during this 2 s period.(c) The change of velocity of the satellite during this time period.arrow_forward
- A 180-lb man and a 120-lb woman stand side by side at the same end of a 300-lb boat, ready to dive, each with a 16-ft/s velocity relative to the boat. Determine the velocity of the boat after they have both dived, if (a) the woman dives first, (b) the man dives first.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_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_forward
- Problem 11.2 Two swimmers A and B, of mass 75 kg and 50 kg, respectively, dive off the end of a 200-kg boat. Each swimmer has a relative horizontal velocity of 3 m/s when leaving the boat. If the boat is initially at rest, determine its final velocity, assuming that (a) the two swimmers dive simultaneously, (b) swimmer A dives first, (c) swimmer B dives first. Answers: all velocities will be between 0.75 m/s <|V|< 1.4 m/sarrow_forwardA 2-kg collar is attached to a spring and slides without friction in a vertical plane along the curved rod ABC . The spring is undeformed when the collar is at C and its constant is 600 N/m. If the collar is released at A with no initial velocity, determine its velocity (a) as it passes through B, (a) as it reaches C.arrow_forwardA 16-Mg jet airplane maintains a constant speed of 774 km/h while climbing at an angle a = 18°. The airplane scoops in air at a rate of 300 kg/s and discharges it with a velocity of 665 m/s relative to the airplane. If the pilot changes to a horizontal flight while maintaining the same engine setting, determine (a) the initial acceleration of the plane, (b) the maximum horizontal speed that will be attained. Assume that the drag due to air friction is proportional to the square of the speed.arrow_forward
- An airline employee tosses two suitcases with weights of 30 lb and 40 lb, respectively, onto a 50-lb baggage carrier in rapid succession. Knowing that the carrier is initially at rest and that the employee imparts a 9-ft/s horizontal velocity to the 30-lb suitcase and a 6-ft/s horizontal velocity to the 40-lb suitcase, determine the final velocity of the baggage carrier if the first suitcase tossed onto the carrier is (a) the 30-lb suitcase, (b) the 40-lb suitcase.arrow_forwardWhile cruising in level flight at a speed of 570 mi/h, a jet airplane scoops in air at a rate of 240 lb/s and discharges it with a velocity of 2200 ft/s relative to the airplane. Determine (a) the power actually used to propel the airplane, (b) the total power developed by the engine, (c) the mechanical efficiency of the airplane.arrow_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
- 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