EBK ENGINEERING MECHANICS
15th Edition
ISBN: 9780137616909
Author: HIBBELER
Publisher: VST
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 12, Problem 85P
The flight path of the helicopter as it takes off from A is defined by the parametric equations x = (2t2) m and y = (0.04t3) m, where t is the time in seconds. Determine the distance the helicopter is from point A and the magnitudes of its velocity and acceleration when t = 10 s.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Car A is traveling at a constant speed of vA = 130 kph at a location where the speed limit is 100 kph. The police officer in car P observes this speed via radar. As Car A passes P, the car uniformly decelerates to the speed limit for 5 seconds and maintained the motion. Meanwhile, the police car begins to accelerate at the constant rate of 6 m/s2 until a velocity of 160 kph is achieved, and that speed is maintained.
Determine the deceleration of car A to reach the speed limit,What is the distance traveled by the police to overtake car A, How long did it take for the police officer to overtake car A?
A particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x =
4.9t² - 1.6t and y = 4.3t² - t³/2.1. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors
make with the x-axis when t = 7.0 s.
Answers: When t = 7.0 s,
V = i
mm/s, ex
i
a =
mm/s², 0x=
i
Mi
=
A particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x =
4.8t² - 3.0t and y = 6.1t²-t3/1.4. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors
make with the x-axis when t = 3.9 s.
Answers: When t = 3.9 s,
V =
a =
M.
mm/s, 0x = i
mm/s², 0x = i
O
Chapter 12 Solutions
EBK ENGINEERING MECHANICS
Ch. 12 - Initially, the car travels along a straight road...Ch. 12 - A ball is thrown vertically upward with a speed of...Ch. 12 - A particle travels along a straight line with a...Ch. 12 - A particle travels along a straight line with a...Ch. 12 - The position of the particle is given by s = (2t2 ...Ch. 12 - A particle travels along a straight line with an...Ch. 12 - A particle moves along a straight line such that...Ch. 12 - A particle travels along a straight line with a...Ch. 12 - Starting from rest, a particle moving in a...Ch. 12 - If a particle has an initial velocity of v0 = 12...
Ch. 12 - A particle travels along a straight line with a...Ch. 12 - A particle travels along a straight line with a...Ch. 12 - Prob. 5PCh. 12 - A particle is moving along a straight line such...Ch. 12 - A particle moves along a straight line with an...Ch. 12 - A particle travels along a straight-line path such...Ch. 12 - Tests reveal that a normal driver takes about 0.75...Ch. 12 - A particle is moving with a velocity of v0 when s...Ch. 12 - A particle is moving along a straight line with an...Ch. 12 - Car B is traveling a distanced ahead of car A....Ch. 12 - The velocity of a particle traveling along a...Ch. 12 - A freight train travels at v = 60(1 et) ft/s,...Ch. 12 - A particle is moving along a straight line such...Ch. 12 - If the effects of atmospheric resistance are...Ch. 12 - When a particle falls through the air, its initial...Ch. 12 - A sphere is fired downwards into a medium with an...Ch. 12 - Prob. 33PCh. 12 - Prob. 34PCh. 12 - A freight train starts from rest and travels with...Ch. 12 - Prob. 36PCh. 12 - Prob. 37PCh. 12 - Prob. 38PCh. 12 - Prob. 39PCh. 12 - An airplane starts from rest, travels 5000 ft down...Ch. 12 - The elevator starts from rest at the first floor...Ch. 12 - The motion of a jet plane just after landing on a...Ch. 12 - Prob. 44PCh. 12 - The vt graph for a particle moving through an...Ch. 12 - The a-s graph for a rocket moving along a straight...Ch. 12 - The jet car is originally traveling at a velocity...Ch. 12 - The v-t graph for a train has been experimentally...Ch. 12 - A motorcycle starts from rest at s = 0 and travels...Ch. 12 - A motorcycle starts from rest at s = 0 and travels...Ch. 12 - The v-t graph for the motion of a car as it moves...Ch. 12 - An airplane lands on the straight runway,...Ch. 12 - Starting from rest at s = 0, a boat travels in a...Ch. 12 - Starting from rest at s = 0, a boat travels in a...Ch. 12 - The speed of a train during the first minute has...Ch. 12 - A man riding upward in a freight elevator...Ch. 12 - Two cars start from rest side by side and travel...Ch. 12 - If the position of a particle is defined as s =...Ch. 12 - The jet plane starts from rest at s = 0 and is...Ch. 12 - Prob. 67PCh. 12 - Prob. 15FPCh. 12 - Prob. 16FPCh. 12 - A particle is constrained to travel along the...Ch. 12 - Prob. 18FPCh. 12 - A particle is traveling along the parabolic path y...Ch. 12 - Prob. 20FPCh. 12 - The ball is kicked from point A with the initial...Ch. 12 - The ball is kicked from point A with the initial...Ch. 12 - Prob. 23FPCh. 12 - Prob. 24FPCh. 12 - A ball is thrown from A. If it is required to...Ch. 12 - Prob. 26FPCh. 12 - If the velocity of a particle is defined as v(t) =...Ch. 12 - The velocity of a particle is v= {3i + (6 2t)j}...Ch. 12 - A particle, originally at rest and located at...Ch. 12 - The velocity of a particle is given by v ={16t2 i...Ch. 12 - The water sprinkler, positioned at the base of a...Ch. 12 - Prob. 74PCh. 12 - Prob. 75PCh. 12 - A particle travels along the curve from A to B in...Ch. 12 - The position of a crate sliding down a ramp is...Ch. 12 - A rocket is fired from rest at x = 0 and travels...Ch. 12 - The particle travels along the path defined by the...Ch. 12 - The motorcycle travels with constant speed v0...Ch. 12 - A particle travels along the curve from A to B in...Ch. 12 - The roller coaster car travels down the helical...Ch. 12 - Pegs A and B are restricted to move in the...Ch. 12 - The van travels over the hill described by y =...Ch. 12 - The flight path of the helicopter as it takes off...Ch. 12 - Determine the minimum initial velocity v0 and the...Ch. 12 - The catapult is used to launch a ball such that it...Ch. 12 - Neglecting the size of the ball, determine the...Ch. 12 - The girl at A can throw a ball at vA = 10 m/s....Ch. 12 - Show that the girl at A can throw the ball to the...Ch. 12 - The ball at A is kicked with a speed vA, = 80ft/s...Ch. 12 - The ball at A is kicked such that A = 30. If it...Ch. 12 - A golf ball is struck with a velocity of 80 ft/s...Ch. 12 - A golf ball is struck with a velocity of 80 ft/s...Ch. 12 - The basketball passed through the hoop even...Ch. 12 - It is observed that the skier leaves the ramp A at...Ch. 12 - It is observed that the skier leaves the ramp A at...Ch. 12 - Determine the horizontal velocity vA of a tennis...Ch. 12 - The missile at A takes off from rest and rises...Ch. 12 - The projectile is launched with a velocity v0....Ch. 12 - Prob. 101PCh. 12 - Prob. 102PCh. 12 - If the dart is thrown with a speed of 10 m/s,...Ch. 12 - Prob. 104PCh. 12 - Prob. 105PCh. 12 - Prob. 106PCh. 12 - Prob. 107PCh. 12 - Prob. 108PCh. 12 - The catapult is used to launch a ball such that it...Ch. 12 - Prob. 27FPCh. 12 - Prob. 28FPCh. 12 - Prob. 29FPCh. 12 - Prob. 30FPCh. 12 - Prob. 31FPCh. 12 - Prob. 32FPCh. 12 - The position of a particle is defined by r = {4(t ...Ch. 12 - The automobile has a speed of 80 ft/s at point A...Ch. 12 - The satellite S travels around the earth in a...Ch. 12 - The car passes point A with a speed of 25 m/s...Ch. 12 - Prob. 122PCh. 12 - Prob. 127PCh. 12 - Prob. 128PCh. 12 - Prob. 129PCh. 12 - Prob. 130PCh. 12 - A boat is traveling along a circular path having a...Ch. 12 - Prob. 132PCh. 12 - Prob. 133PCh. 12 - Prob. 134PCh. 12 - When t = 0, the train has a speed of 8 m/s, which...Ch. 12 - The ball is ejected horizontally from the tube...Ch. 12 - The race car has an initial speed vA = 15 m/s at...Ch. 12 - Particles A and B are traveling counter-clockwise...Ch. 12 - Prob. 146PCh. 12 - Prob. 149PCh. 12 - The train passes point A with a speed of 30 m/s...Ch. 12 - The particle travels with a constant speed of 300...Ch. 12 - Prob. 152PCh. 12 - If the speed of the crate at A is 15 ft/s, which...Ch. 12 - The car has a speed of 55 ft/s. Determine the...Ch. 12 - The platform is rotating about the vertical axis...Ch. 12 - Peg P is driven by the fork link OA along the...Ch. 12 - Prob. 36FPCh. 12 - Prob. 37FPCh. 12 - Prob. 38FPCh. 12 - An airplane is flying in a straight line with a...Ch. 12 - The small washer is sliding down the cord OA. When...Ch. 12 - If a particle moves along a path such that r = (2...Ch. 12 - Prob. 162PCh. 12 - The time rate of change of acceleration is...Ch. 12 - A particle moves in the x y plane such that its...Ch. 12 - At the instant shown, the man is twirling a hose...Ch. 12 - The rod OA rotates clockwise with a constant...Ch. 12 - Determine the magnitude of the acceleration of the...Ch. 12 - The rod OA rotates counterclockwise with a...Ch. 12 - Determine the magnitude of the acceleration of the...Ch. 12 - Prob. 189PCh. 12 - Determine the velocity of block D if end A of the...Ch. 12 - Prob. 40FPCh. 12 - Prob. 41FPCh. 12 - Prob. 42FPCh. 12 - Prob. 43FPCh. 12 - Prob. 44FPCh. 12 - If the end of the cable at A is pulled down with a...Ch. 12 - The motor at C pulls in the cable with an...Ch. 12 - Determine the displacement of the log if the truck...Ch. 12 - Determine the constant speed at which the cable at...Ch. 12 - Starting from rest, the cable can be wound onto...Ch. 12 - If the end A of the cable is moving at vA = 3 m/s,...Ch. 12 - Determine the time needed for the load at B to...Ch. 12 - The cable at A is being drawn toward the motor at...Ch. 12 - Determine the speed of the block at B.Ch. 12 - The roller at A is moving with a velocity of A = 4...Ch. 12 - Prob. 213PCh. 12 - At the instant shown, the car at A is traveling at...Ch. 12 - The motor draws in the cord at B with an...Ch. 12 - If block B is moving down with a velocity vB and...Ch. 12 - Two planes, A and B, are flying at the same...Ch. 12 - Prob. 219PCh. 12 - The boat can travel with a speed of 16 km/h in...Ch. 12 - Two boats leave the pier P at the same time and...Ch. 12 - Prob. 222PCh. 12 - At the instant shown, car A has a speed of 20...Ch. 12 - Cars A and B are traveling around the circular...Ch. 12 - At the instant shown, cars A and B are traveling...Ch. 12 - Prob. 228PCh. 12 - Prob. 230PCh. 12 - Prob. 232PCh. 12 - Prob. 1RPCh. 12 - Prob. 2RPCh. 12 - Prob. 3RPCh. 12 - Prob. 4RPCh. 12 - Prob. 5RPCh. 12 - Prob. 6RPCh. 12 - Prob. 7RPCh. 12 - Prob. 8RPCh. 12 - Prob. 9RPCh. 12 - Prob. 10RPCh. 12 - Prob. 11RP
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.Similar questions
- The rectangular coordinates of a particle which moves with curvilinear motion are given by x = 10.75t +2.25t² - 0.45t³ and y = 6.90 + 17.43t - 2.62t², where x and y are in millimeters and the time t is in seconds, beginning from t = 0. Determine the velocity v and acceleration a of the particle when t = 8 s. Also, determine the first time that the velocity of the particle makes an angle of 30° with the positive x-axis. Answers: V = a = 17.1 10.75 i + i 5.24 i+ i 17.43 j) mm/s j) mm/s²arrow_forwardThe rectangular coordinates of a particle which moves with curvilinear motion are given by x= 10.00t+1.00t² - 0.55+³ and y = 6.32 + 10.10t - 2.22t², where x and y are in millimeters and the time t is in seconds, beginning from t = 0. Determine the velocity v and acceleration a of the particle when t = 8 s. Also, determine the first time that the velocity of the particle makes an angle of 18° with the positive x-axis. Answers: V = a = (i t = tel it i i+i S j) mm/s j) mm/s²arrow_forwardA particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x = 2.5t2 - 3.2t and y = 1.6t2 - t³/4.7. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors make with the x-axis when t= 3.5 s. Answers: When t = 3.5 s, V = i mm/s, 8x mm/s?, 0x a =arrow_forward
- Applying principles of dynamics A freighter is moving at a speed of 8 nautical miles per hour. The engines then had to be suddenly stopped. If it takes 10 minutes for the freighter to reduce its speed to 3 knots, determine the distance moved by the ship and its speed at the end of this interval. The deceleration of the ship is propor-tional to the square of its speed such that a = -kV^2.arrow_forwardWhen the effect of aerodynamic drag is included, the y-acceleration of a baseball moving vertically upward is au = -g - kv², while the acceleration when the ball is moving downward is ad = -g + kv², where k is a positive constant and v is the speed in feet per second. If the ball is thrown upward at 94 ft/sec from essentially ground level, compute its maximum height h and its speed vf (a positive number) upon impact with the ground. Take k to be 0.0017 ft¹ and assume that g is constant. au=-g-ku² y 1 194 ft/sec Answers: h = Vf= i i ad=-g+kv2 h ft ft/secarrow_forwardThe velocity of a particle moving in the x-y plane is given by (5.92i +4.07j) m/s at time t = 5.92 s. Its average acceleration during the next 0.019 s is (2.2i + 3.2j) m/s². Determine the velocity v of the particle at t = 5.939 s and the angle 8 between the average- acceleration vector and the velocity vector at t = 5.939 s. Answers: v = (i 0 = wpad i+ IN j) m/sarrow_forward
- The rectangular coordinates of a particle which moves with curvilinear motion are given by x = 9.75t + 1.25t²-0.60t3 and y=6.12 + 10.89t-2.01t², where x and y are in millimeters and the time t is in seconds, beginning from t= 0 Determine the velocity v and acceleration of the particle when t-7s. Also, determine the first time that the welocity of the particle makes an angle of 27" with the positive-anis V= 13 25 i i [ mmsarrow_forwardA particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x = 3.2t2 - 1.3t and y = 4.2t2 - t/3.6. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors make with the x-axis when t = 4.8 s. Answers: Whent= 4.8 s, V = i mm/s, O, = i a = i mm/s?, ex = iarrow_forwardA particle moving in the x-y plane has a velocity v = 6.821 +3.07j m/s at a certain instant. If the particle then encounters a constant acceleration a = 0.69j m/s², determine the amount of time which must pass before the direction of the tangent to the trajectory of the particle has been altered by 24° Answer: t = i Sarrow_forward
- A particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x = 5.6t2 - 3.7t and y = 5.7t2 - t3/1.7. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors make with the x-axis when t = 5.5 s.Answers: When t = 5.5 s,arrow_forwardA A particle is moving along a curve. Its x position is described by x = t² m while its y position is given by the function y = 2 + t4 m. Determine the following: a. Sketch an x-y plot of the particle's path, showing the starting position (at t = 0) of and the direction taken by the particle b. At t= 1 sec, determine the velocity and acceleration vectors of the particle. (Express in Cartesian vector form) c. At t = 1 sec, determine the normal and tangential components of the acceleration. Show the vector diagram of the components. d. Determine the magnitude of the acceleration at t = 1 sec.arrow_forwardA particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x = 2.9t2 - 6.6t and y = 4.5t2 - t3/6.8. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors make with the x-axis when t = 1.3 s.Answers: When t = 1.3 s,arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- 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
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Dynamics - Lesson 1: Introduction and Constant Acceleration Equations; Author: Jeff Hanson;https://www.youtube.com/watch?v=7aMiZ3b0Ieg;License: Standard YouTube License, CC-BY