Explanation Given: The maximum and minimum distance from center of the planet is shown in Figure (1). The mass of the planet M = 0.6 ( 5.976 × 10 24 kg ) . The gravitational constant is G = 66.73 × 10 − 12 m 3 / kg ⋅ s 2 From Figure (1) write the value for minimum distance r p . r p = 6 Mm 10 6 m 1 Mm = 6 ( 10 6 ) m From Figure (1) write the value for maximum distance r a . r a = 100 Mm 10 6 m 1 Mm = 100 ( 10 6 ) m Write the expression for the minimum distance from the centre of Planet. r a = r 0 2 G M ( r 0 υ 0 2 ) − 1 (I) Here, minimum distance from the center of planet is r 0 and the initial speed of the rocket υ 0 and the gravitational constant is G and mass of the planet is M . From Figure (1) write the equation for the h . h = r p υ p = r a υ a h = r p υ B = r a υ A ' (II) Here, h is constant at any positions of the orbit , the speed of the rocket at apogee is υ a , the speed of the rocket at perigee is υ p , r p is the minimum distance from the center of planet or perigee and r a is the orbit maximum distance from the center of planet or apogee. Write the expression for period of elliptical orbit. T = π r p υ p ( r p + r a ) r p r a (III) Here, period is T , r p is minimum distance from the center of planet or perigee and r a is the maximum distance from the center of planet or apogee. Write the expression for time required to travel from A to A ' . t = T 2 (IV) Here, period is T and time is t . Conclusion: Since, r 0 = r p and υ 0 = υ p . Substitute r p for r 0 and υ p for υ 0 in Equation (I). r a = r 0 2 G M ( r 0 υ 0 2 ) − 1 r a = r p 2 G M ( r p υ p 2 ) − 1 2 G M e ( r p υ p 2 ) M = r p r a + 1 2 G M ( r p υ p 2 ) = r p + r a r a υ p = 2 G M r a r p ( r p + r a ) (V). Since, υ p = υ B . Substitute υ B for υ p , [ 100 ( 10 6 ) m ] for r a , [ 6 ( 10 6 ) m ] for r p , 66

Engineering Mechanics: Dynamics (14th Edition)

14th Edition

ISBN: 9780133915389

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 13.7, Problem 130P

To determine

The required free-flight speed rocket must have at A' and the time t required for the rocket to land, going from A' to B' .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.7, Problem 129P

Chapter 13.7, Problem 131P

Students have asked these similar questions

The 12-Mg truck drives onto the 396-Mg barge from the dock at 17 km/h and brakes to stop on the deck. The barge is free to move in the water, which offers negligible resistance to motion at low speeds. Calculate the speed of the barge after the truck has come to rest on it. 17 km/h 396 Mg 12 Mg Answer: v = km/h

The 245-kg glider Bis being towed by airplane A, which is flying horizontally with a constant speed of v = 183 km/h. The tow cable has a length r = 59 m and may be assumed to form a straight line. The glider is gaining altitude and when e reaches 14°, the angle is increasing at the constant rate 0 = 8 deg/s. At the same time the tension in the tow cable is 2370 N for this position. Calculate the aerodynamic lift L and drag D acting on the glider. Assume o = 10°. D B A

The 12-Mg truck drives onto the 366-Mg barge from the dock at 27 km/h and brakes to stop on the deck. The barge is free to move in the water, which offers negligible resistance to motion at low speeds. Calculate the speed of the barge after the truck has come to rest on it.

Chapter 13 Solutions

Engineering Mechanics: Dynamics (14th Edition)

Ch. 13.4 - In each case, determine its velocity when t = 2 s...Ch. 13.4 - In each case, determine its velocity at s = 8 m if...Ch. 13.4 - Determine the initial acceleration of the 10-kg...Ch. 13.4 - Write the equations of motion in the x and y...Ch. 13.4 - The motor winds n the cable with a constant...Ch. 13.4 - If motor M exerts a force of F = (10t2 + 100) N on...Ch. 13.4 - A spring of stiffness k = 500 N/m is mounted...Ch. 13.4 - The spring has a stiffness k = 200 N/m and is...Ch. 13.4 - Block B rests upon a smooth surface. If the...Ch. 13.4 - The 6-lb particle is subjected to the action of...

Ch. 13.4 - The two boxcars A and B have a weight of 20 000 lb...Ch. 13.4 - If the coefficient of kinetic friction between the...Ch. 13.4 - If the 50-kg crate starts from rest and achieves a...Ch. 13.4 - If blocks A and B of mass 10 kg and 6 kg...Ch. 13.4 - The 10-lb block has a speed of 4 ft/s when the...Ch. 13.4 - The 10-lb block has a speed of 4 ft/s when the...Ch. 13.4 - The speed of the 3500-lb sports car is plotted...Ch. 13.4 - The conveyor belt is moving at 4 m/s. If the...Ch. 13.4 - The conveyor belt is designed to transport...Ch. 13.4 - Determine the time needed to pull the cord at B...Ch. 13.4 - Cylinder B has a mass m and is hoisted using the...Ch. 13.4 - Block A has a weight of 8 lb and block B has a...Ch. 13.4 - The 2-Mg truck is traveling at 15 m/s when the...Ch. 13.4 - The motor lifts the 50-kg crate with an...Ch. 13.4 - The 75-kg man pushes on the 150-kg crate with a...Ch. 13.4 - The coefficient of kinetic friction is k, and the...Ch. 13.4 - A 40-lb suitcase slides from rest 20 ft down the...Ch. 13.4 - Solve Prob. 13-18 if the suitcase has an initial...Ch. 13.4 - If the coefficient of kinetic friction between...Ch. 13.4 - The conveyor belt delivers each 12-kg crate to the...Ch. 13.4 - The 50-kg block A is released from rest. Determine...Ch. 13.4 - If the supplied force F = 150 N, determine the...Ch. 13.4 - A 60-kg suitcase slides from rest 5 m down the...Ch. 13.4 - Solve Prob. 13-24 if the suitcase has an initial...Ch. 13.4 - The 1.5 Mg sports car has a tractive force of F =...Ch. 13.4 - The conveyor belt is moving downward at 4 m/s. If...Ch. 13.4 - At the instant shown the 100-lb block A is moving...Ch. 13.4 - Determine the velocity of the 200-lb crate when t...Ch. 13.4 - Determine the velocity of the 400-kg crate A when...Ch. 13.4 - The tractor is used to lift the 150-kg load B with...Ch. 13.4 - If the tractor travels to the right with an...Ch. 13.4 - Block A and B each have a mass m. Determine the...Ch. 13.4 - The 4-kg smooth cylinder is supported by the...Ch. 13.4 - The coefficient of static friction between the...Ch. 13.4 - If the spring is unstretched when s = 0 and the...Ch. 13.4 - Neglecting the mass of the rope and pulley, and...Ch. 13.4 - Determine the force in the cable when t = 5 s, if...Ch. 13.4 - An electron of mass m is discharged with an...Ch. 13.4 - The 400-lb cylinder at A is hoisted using the...Ch. 13.4 - What is their velocity at this instant?Ch. 13.4 - Block A has a mass mA and is attached to a spring...Ch. 13.4 - A parachutist having a mass m opens his parachute...Ch. 13.4 - Neglect the mass of the motor and pulleys.Ch. 13.4 - If the force exerted on cable AB by the motor is F...Ch. 13.4 - Blocks A and B each have a mass m. Determine the...Ch. 13.4 - Blocks A and Beach have a mass m. Determine the...Ch. 13.4 - If the board AC pushes on the block at an angle ...Ch. 13.4 - If a horizontal force P = 12lb is applied to block...Ch. 13.4 - A freight elevator, including its load, has a mass...Ch. 13.4 - The block A has a mass mA and rests on the pan B,...Ch. 13.5 - P13-5.Set up the n, t axes and write the equations...Ch. 13.5 - P13-6.Set up the n, b, t axes and write the...Ch. 13.5 - The block rests at a distance of 2 m from the...Ch. 13.5 - Prob. 8FP Ch. 13.5 - A pilot weighs 150 lb and is traveling at a...Ch. 13.5 - The sports car is traveling along a 30 banked road...Ch. 13.5 - If the 10-kg ball has a velocity of 3m/ s when it...Ch. 13.5 - The motorcycle has a mass of 0.5 Mg and a...Ch. 13.5 - Prob. 52P Ch. 13.5 - Prob. 53P Ch. 13.5 - The 2-kg block B and 15-kg cylinder A are...Ch. 13.5 - Determine the maximum constant speed at which the...Ch. 13.5 - Cartons having a mass of 5 kg are required to move...Ch. 13.5 - Prob. 57P Ch. 13.5 - Prob. 58P Ch. 13.5 - Prob. 59P Ch. 13.5 - Prob. 60P Ch. 13.5 - At the instant B = 60, the boys center of mass G...Ch. 13.5 - A girl having a mass of 25 kg sits at the edge of...Ch. 13.5 - The pendulum bob B has a weight of 5 lb and is...Ch. 13.5 - The pendulum bob B has a mass m and is released...Ch. 13.5 - Determine the constant speed of the passengers on...Ch. 13.5 - A motorcyclist in a circus rides his motorcycle...Ch. 13.5 - The vehicle is designed to combine the feel of a...Ch. 13.5 - The 0.8-Mg car travels over the hill having the...Ch. 13.5 - The 0.8-Mg car travels over the hill having the...Ch. 13.5 - When it reaches the curved portion AB, it is...Ch. 13.5 - Determine the resultant normal and frictional...Ch. 13.5 - If he rotates about the z axis with a constant...Ch. 13.5 - Determine the maximum speed at which the car with...Ch. 13.5 - Determine the maximum constant speed at which the...Ch. 13.5 - The box has a mass m and slides down the smooth...Ch. 13.5 - Prove that if the block is released from rest at...Ch. 13.5 - The cylindrical plug has a weight of 2 lb and it...Ch. 13.5 - When crossing an intersection, a motorcyclist...Ch. 13.5 - The airplane, traveling at a constant speed of 50...Ch. 13.5 - The 2-kg pendulum bob moves in the vertical plane...Ch. 13.5 - The 2-kg pendulum bob moves in the vertical plane...Ch. 13.5 - If it has a speed of 1.5 m/s when y = 0.2 m,...Ch. 13.5 - The ball has a mass m and is attached to the cord...Ch. 13.6 - If the attached spring has a stiffness k = 2...Ch. 13.6 - Determine the constant angular velocity of the...Ch. 13.6 - If = ( t2) rad, where t is in seconds, determine...Ch. 13.6 - The 2-Mg car is traveling along the curved road...Ch. 13.6 - The 0.2-kg pin P is constrained to move in the...Ch. 13.6 - If the cam is rotating at a constant rate of 6...Ch. 13.6 - Determine the magnitude of the resultant force...Ch. 13.6 - Determine the magnitude of the unbalanced force...Ch. 13.6 - Rod OA rotates counterclockwise with a constant...Ch. 13.6 - The boy of mass 40 kg is sliding down the spiral...Ch. 13.6 - Using a forked rod, a 0.5-kg smooth peg P is...Ch. 13.6 - The arm is rotating at a rate of = 4 rad/s when ...Ch. 13.6 - If arm OA rotates with a constant clockwise...Ch. 13.6 - Determine the normal and frictional driving forces...Ch. 13.6 - A smooth can C, having a mass of 3 kg, is lifted...Ch. 13.6 - Prob. 96P Ch. 13.6 - Prob. 97P Ch. 13.6 - The particle has a mass of 0.5 kg and is confined...Ch. 13.6 - A car of a roller coaster travels along a track...Ch. 13.6 - The 0.5-lb ball is guided along the vertical...Ch. 13.6 - The ball of mass misguided along the vertical...Ch. 13.6 - Using a forked rod, a smooth cylinder P, having a...Ch. 13.6 - The pilot of the airplane executes a vertical loop...Ch. 13.6 - The collar has a mass of 2 kg and travels along...Ch. 13.6 - The particle has a mass of 0.5 kg and is confined...Ch. 13.6 - Solve Prob. 13-105 If the arm has an angular...Ch. 13.6 - The forked rod is used to move the smooth 2-lb...Ch. 13.6 - Prob. 108P Ch. 13.6 - Rod OA rotates counterclockwise at a constant...Ch. 13.6 - Solve Prob. 13-109 if motion is in the vertical...Ch. 13.7 - If his speed is a constant vP = 80 ft/s, determine...Ch. 13.7 - The earth has an orbit with eccentricity 0.0167...Ch. 13.7 - Prob. 114P Ch. 13.7 - Determine the speed of a satellite launched...Ch. 13.7 - Prob. 116P Ch. 13.7 - Prove Keplers third law of motion. Hint: Use Eqs....Ch. 13.7 - Prob. 118P Ch. 13.7 - Prob. 119P Ch. 13.7 - Determine the constant speed of satellite S so...Ch. 13.7 - Prob. 121P Ch. 13.7 - Prob. 122P Ch. 13.7 - Prob. 123P Ch. 13.7 - Prob. 124P Ch. 13.7 - The rocket is traveling around the earth in free...Ch. 13.7 - Prob. 127P Ch. 13.7 - Prob. 128P Ch. 13.7 - Prob. 129P Ch. 13.7 - Prob. 130P Ch. 13.7 - The rocket is traveling around the earth in free...Ch. 13.7 - Prob. 132P Ch. 13.7 - Prob. 3CP Ch. 13.7 - If the trailer has a mass of 250 kg and coasts 45...Ch. 13.7 - The coefficient of kinetic friction between the...Ch. 13.7 - Block B rests on a smooth surface. If the...Ch. 13.7 - If the motor draws in the cable at a rate of v =...Ch. 13.7 - The ball has a mass of 30 kg and a speed v = 4 m/s...Ch. 13.7 - If the coefficient of static friction between the...Ch. 13.7 - If at the instant it reaches point A it has a...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The required free-flight speed rocket must have at A ' and the time t required for the rocket to land, going from A ' to B ' .

Solution Summary: The author determines the required free-flight speed rocket must have at A' and the time t required for the rocket to land.

Concept explainers

Videos

The required free-flight speed rocket must have at A' and the time t required for the rocket to land, going from A' to B' .

Want to see the full answer?

Chapter 13 Solutions