Concept explainers
(a)
The angle
Answer to Problem 11.112P
Explanation of Solution
Given information:
Initial velocity
Rocket lands at distance
For a uniformly accelerated motion,
In above equation,
Calculation:
For horizontal motion,
Therefore,
For vertical motion,
Therefore,
But, we know that,
Substitute,
Solve further,
But,
Therefore,
Solve to find
Therefore,
To find the angle
Therefore,
Conclusion:
The value of angle
(b)
The maximum height reached by the rocket?
Answer to Problem 11.112P
Explanation of Solution
Given information:
Initial velocity
Rocket lands at distance
For a uniformly accelerated motion,
In above equation,
Calculation:
At maximum height,
Therefore,
We get,
To find maximum height,
Substitute,
Conclusion:
The maximum height reached by the rocket is equal to
(c)
The duration of flight?
Answer to Problem 11.112P
Explanation of Solution
Given information:
Initial velocity
Rocket lands at distance
For a uniformly accelerated motion,
In above equation,
Calculation:
For horizontal motion,
Therefore,
For vertical motion,
Therefore,
But, we know that,
Substitute,
Solve further,
But,
Therefore,
Solve to find
Therefore,
Conclusion:
The possible duration of flight is equal to
Want to see more full solutions like this?
Chapter 11 Solutions
Vector Mechanics For Engineers
- A piece of mass M is hung by a string of length L . A ball of mass m = M / 4 has a velocity V• when it hits the piece and sinks into it. As soon as the progress of the bullet in the piece stops completely, the string tension is 2.5Mg. What is the velocity V•?arrow_forwardA 2-oz pellet shot vertically from a spring-loaded pistol on the surface of the earth rises to a height of 300 ft. The same pellet shot from the same pistol on the surface of the moon rises to a height of 1900 ft. Determine the energy dissipated by aerodynamic drag when the pellet is shot on the surface of the earth. (The acceleration of gravity on the surface of the moon is 0.165 times that on the surface of the earth.)arrow_forward3.) The thrust of a 500-lb rocket sled varies with time as shown below. If the sled starts from rest and travels along a straight, horizontal track, determine its velocity when the rocket burns out. Assume negligible friction.arrow_forward
- A 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_forwardGayle runs at a speed of 4.10 m/s and dives on a sled, initially at rest on the top of a frictionless snow-covered hill. After she has descended a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back and together they continue down the hill. What is their speed at the bottom of the hill if the total vertical drop is 15.0 m? Gayle's mass is 46.5 kg, the sled has a mass of 5.25 kg and her brother has a mass of 30.0 kg.arrow_forwardA 200-lb bungee jumper jumps from a bridge 130 ft above a river. The bungee cord has an unstretched length of 60 ft and has a spring constant k = 14 lb/ft. (a) How far above the river is the jumper when the cord brings him to a stop? (b) What maximum force does the cord exert on him? (c) What is the maximum velocity does the jumper reach?arrow_forward
- Two objects m1 = 5.15 kg and m2 = 2.95 kg)are connected by a light string passing over a light, frictionless pulley as in the figure below. The 5.15-kg object is released from rest at a point h = 4.00 m above the table. (a) Determine the speed of each object when the two pass each other. m/s(b) Determine the speed of each object at the moment the 5.15-kg object hits the table. m/s(c) How much higher does the 2.95-kg object travel after the 5.15-kg object hits the table? marrow_forwardA 20-kg base satellite deploys three sub-satellites, each which has its own thrust capabilities, to perform research on tether propulsion. The masses of sub-satellites A, B, and C are 4 kg, 6 kg, and 8 kg, respectively, and their velocities expressed in m/s are given by vA = 4i - 2j +2k, vB = i + 4j, vC = 2i + 2j +4k. At the instant shown, what is the angular momentum HO of the system about the base satellite?arrow_forwardThe parasailing system shown uses a winch to pull the rider in towards the boat, which is travelling with a constant velocity. During the interval when 0 is between 20° and 40° (where t= 0 at 0= 20°), the angle increases at the constant rate of 2°/s. During this time, the length of the rope is defined by the relationship r= 125 - where r and t are expressed in meters and seconds, respectively. At the instant when the rope makes a 30° angle with the water, the tension in the rope is 18 kN. At this instant, what is the magnitude and direction of the force of the parasail on the 75 kg parasailor?arrow_forward
- A 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_forwardThe triple jump is a track-and-field event in which an athlete gets a running start and tries to leap as far as he can with a hop, step, and jump. Shown in the figure is the initial hop of the athlete. Assuming that he approaches the takeoff line from the left with a horizontal velocity of 10 m/s, remains in contact with the ground for 0.18 s, and takes off at a 50° angle with a velocity of 12 m/s, determine the vertical component of the average impulsive force exerted by the ground on his foot. Give your answer in terms of the weight W of the athlete.arrow_forwardThe second stage of a two-stage rocket weighs 2000 lb (empty) and is launched from the first stage with a velocity of 3000 mi/h. The fuel in the second stage weighs 1000 lb. If it is consumed at the rate of 50lb/s and ejected with a relative velocity of 8000 ft/s, determine the acceleration of the second stage just after the engine is fired. What is the rocket’s acceleration just before all the fuel is consumed? Neglect the effect of gravitation.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