Concept explainers
Determine the distance traveled by the spacecraft of Prob. 14.97 during the rocket engine firing, knowing that its initial speed was 7500 ft/s and the duration of the firing was 60 s.
14.97 The 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.
Fig. P14.97 and P14.98
Find the distance travelled by the spacecraft.
Answer to Problem 14.99P
The distance travelled by the spacecraft is
Explanation of Solution
Given information:
The initial speed of the spacecraft is
The duration of firing is
The change in velocity is
The gross weight of the spacecraft is
The fuel consumed rate is
Calculation:
Calculate the thrust force
Calculate the mass
Calculate the acceleration
Substitute
Substitute
Calculate the velocity
Substitute
Calculate the displacement
Integrate both sides of the Equation (2) as shown below.
Consider
Differentiate both sides of the Equation (4) as shown below.
Substitute z for
Substitute
Calculate the velocity
Substitute
Consider the acceleration due to gravity
Calculate the gross mass of the spacecraft
Substitute
Consider that the mass of the fuel
Substitute
Calculate the mass
Substitute
Consider the initial displacement
Calculate the relative velocity
Substitute
Calculate distance travelled by the spacecraft
Substitute
Therefore, the distance travelled by the spacecraft is
Want to see more full solutions like this?
Chapter 14 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Additional Engineering Textbook Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Fundamentals of Aerodynamics
Mechanics of Materials, 7th Edition
Fluid Mechanics Fundamentals And Applications
DeGarmo's Materials and Processes in Manufacturing
Applied Statics and Strength of Materials (6th 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 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_forwardA circular reentrant orifice (also called Borda’s mouthpiece) of diameter D is placed at a depth h below the surface of a tank. Knowing that the speed of the issuing stream is v= 2gh and assuming that the speed of approach v1 is zero, show that the diameter of the stream is d= DI 2. (Hint: Consider the section of water indicated, and note that P is equal to the pressure at a depth h multiplied by the area of the orifice.)arrow_forward
- In a game of pool, ball A is moving with the velocity v0 = v0i when it strikes balls B and C , which are at rest side by side. Assuming frictionless surfaces and perfectly elastic impact (i.e., conservation of energy), determine the final velocity of each ball, assuming that the path of A is (a) perfectly centered and that A strikes B and C simultaneously, (b) not perfectly centered and that A strikes B slightly before it strikes C.arrow_forwardA helicopter flying with a velocity of 160km/h at elevation 500m above sea level dropped supplies to hit the barracks situated at elevation 200m above sea level. Determine the distance, in meters, from the barracks the supplies should be dropped so that they will fall within the barracks site.arrow_forwardShow that the speeds of a projectile are the same at any two pointsin its path which are at the same elevation.arrow_forward
- Packages are thrown down an incline at A with a velocity of 1 m/s. The packages slide along the surface ABC to a conveyor belt which moves with a velocity of 2 m/s. Knowing that μk = 0.25 between the packages and the surface ABC , determine the distance d if the packages are to arrive at C with a velocity of 2 m/s.arrow_forwardA meteor starts from rest at a very great distance from the earth. Knowing that the radius of the earth is 6370 km and neglecting all forces except the gravitational attraction of the earth, determine the speed of the meteor (a) when it enters the ionosphere at an altitude of 1000 km, (b) when it enters the stratosphere at an altitude of 50 km, (c) when it strikes the earth’s surface.arrow_forwardTwo identical hockey pucks are moving on a hockey rink at the same speed of 3 m/s and in perpendicular directions when they strike each other as shown. Assuming a coefficient of restitution e= 0.9, determine the magnitude and direction of the velocity of each puck after impact.arrow_forward
- Boxes are transported by a conveyor belt with a velocity v0 to a fixed incline at A where they slide and eventually fall off at B. Knowing that μk = 0.40, determine the velocity of the conveyor belt if the boxes are to have zero velocity at B.arrow_forwardPackages in an automobile parts supply house are transported to the loading dock by pushing them along on a roller track with very little friction. At the instant shown, packages B and c are at rest, and package A has a velocity of 2 m/s. Knowing that the coefficient of restitution between the packages is 0.3, determine (a) the velocity of package C after A hits B and B hits C, (b) the velocity of A after it hits B for the second time.arrow_forwardA 1.5-lb ball that can slide on a horizontal frictionless surface is attached to a fixed point O by means of an elastic cord of constant k= 1 lb/in. and undeformed length 2 ft. The ball is placed at point A, 3 ft from O , and given an initial velocity v0 perpendicular to OA ., allowing the ball to come within a distance d = 9 in. of point O after the cord has become slack. Determine (a) the initial speed v0 of the ball, (b) its maximum speed.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