Concept explainers
(a)
The distance from the center of Venus to point
Answer to Problem 12.106P
The distance from the center of Venus to point
Explanation of Solution
Given information:
If the trajectory is an elliptical orbit,
Calculation:
Consider the first transfer elliptical orbit,
Consider the first transfer elliptical orbit,
Since,
The distance from the center of Venus to point
(b)
The amounts by which the velocity of the probe should be reduced at
Answer to Problem 12.106P
The velocity reduction at point
The velocity reduction at point
Explanation of Solution
Given information:
Angular momentum of a unit mass,
If the trajectory is an elliptical orbit,
Initial velocity corresponding to a circular orbit,
Calculation:
From Part (a),
Consider the first transfer elliptical orbit,
Then consider the second transfer elliptical orbit,
Since,
Applying angular momentum equation for second elliptic orbit,
Therefore the velocity reduction at point
Consider the second transfer elliptical orbit,
Then consider the circular orbit at
Since,
Therefore, the velocity reduction at point
Want to see more full solutions like this?
Chapter 12 Solutions
Vector Mechanics For Engineers
- A particle moves so that its position vector r at timet is r = a cos wt + b sin wt, where w is a constant and a and b are constant vectors. Show that (a) r i is independent of t, (b) the acceleration is everywhere towards the origin and proportional to T.arrow_forwardFrom a photograph of a homeowner using a snowblower, it is determined that the radius of curvature ofthe trajectory of the snow was 30 ft as the snow left the discharge chute at A. Determine (a) the dischargevelocity v A of the snow, (b) the radius of curvature of the trajectory at its maximum height.arrow_forwardProblem (3): Block A moves down with a constant velocity of 2 m/s. Determine: •D (a) The velocity of block C. (b) The velocity of collar B relative to block A. (c) The relative velocity portion D of the cable with respect to block A. B Aarrow_forward
- A golfer hits a golf ball from point A with an initial velocity of 50 m/s at an angle of 25° with the horizontal. Determine the radius of curvature of the trajectory described by the ball (a) at point A, (b) at the highest point of the trajectory.arrow_forwardPROBLEM 3.5 A ball is shot at a ground level at angle of 60 degrees with the horizontal with an initial velocity of 150 m/s. Determine the height of the ball after 4 sec. 6. с. 700 m d. 800 m а. 500 m b. 600 marrow_forwardIn order to uncoil electrical wire from a 0.6-m-radius spool fixed to a truck, a worker drives to the left with a speed of vA = 5 m/s. At the same time, a second worker holds the cable as he walks to the right with a speed of vB = 3 m/s. Knowing that at the instant shown the thickness of wire on the spool is 40 mm, determine (a) the instantaneous center of rotation of the spool, (b) the velocity of point D on the inside of the spool.arrow_forward
- PROBLEM 3.12 An object is launched at a speed of 20.0 m/s from the top of a tall tower. The height y of the object with respect to the base of the tower as a function of the timet elapsed from launch is y(t) = -4.90t² + 19.32t + 60, where y is in meters and t is in seconds. Determine: 13. the height H of the tower. 50 m c. 70 m d. 80 m а. b. 60 m 14. the launch angle. с. 75.35° d. 77.35° а. 71.35° b. 73.35° 15. the horizontal distance traveled by the object before it hits the ground. с. 32.28 m d. 34.28 m a. 28.28 m b. 30.28 marrow_forwardCar A with a constant velocity of 6.1 ft/s is heading east and in an instant that Car B with an initial velocity of 2.75 ft/s is traveling southwest at a constant rate of 0.05 ft/s2. The bearing of Car B from Car A is 30 deg north of east and the distance between them is 4800 ft. (a) Prove whether or not both Cars will collide in 5 mins. (b) What is the distance between the two cars in 10 mins? Show free body diagram.arrow_forward17. Three stones A, B and C are projected with same speed. A is thrown upwards B is thrown horizontally & C is thrown downwards from a building. When the distance between stone A & C becomes 10 m, then distance between A and B will be - (A) 10 m (C) 5√2 (B) 5 m (D) 10√2arrow_forward
- A long-range ballistic trajectory between points A and B on the earth’s surface consists of a portion of an ellipse with the apogee at point C. Knowing that point C is 1500 km above the surface of the earth and the range Rφ of the trajectory is 6000 km, determine (a) the velocity of the projectile at C, (b) the eccentricity ε of the trajectory.arrow_forwardIn slow pitch softball, the underhand pitch must reach a maximum height of between 1.8 m and 3.7 m above the ground. A pitch is made with an initial velocity vo with a magnitude of 13 m/s at an angle of 33° with the horizontal. Determine (a) if the pitch meets the maximum height requirement, (b) the height of the ball as it reaches the batter.arrow_forwardIf two bodies A and B are projected upwards such that the velocity of A is double the velocity of B, then the height to which the body A will rise will be.. the height to which the body B will rise (a) two times (b) four times (c) eight timesarrow_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