Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9781259639272
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 11.5, Problem 11.163P

During a parasailing ride, the boat is traveling at a constant 30 km/hr with a 200-m long tow line. At the instant shown, the angle between the line and the water is 30° and is increasing at a constant rate of 2°/s. Determine the velocity and acceleration of the parasailer at this instant.

Fig. P11.163 and P11.164

Chapter 11.5, Problem 11.163P, During a parasailing ride, the boat is traveling at a constant 30 km/hr with a 200-m long tow line.

Expert Solution & Answer
Check Mark
To determine

The velocity (v) and acceleration (a) of the parasailer at this instant.

Answer to Problem 11.163P

The velocity (v) and acceleration (a) of the parasailer at this instant are 13.280m/s(27.08°)_ and 0.2437m/s(30.00°)_ respectively.

Explanation of Solution

Given Information:

The boat is traveling at a constant speed (vB) of 30km/hr.

The radius (r) of tow line is 200m.

The angle (θ) between the line and the water is 30° and increasing at a constant (θ˙) rate of 2°/s.

Calculation:

Convert the kilometer per hour to meter per second.

Consider (vB):

(vB)=30km/hr×1000m1km×1hr3600sec=8.333m/s

Show the Free body diagram of parasailer and boat as in Figure (1).

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics, Chapter 11.5, Problem 11.163P

Write the velocity (vB) of the boat in term of vector:

vB=8.333im/s

The acceleration vector of the boat is as follows:

aB=0

Differentiate angle (θ˙) with respective to time (t).

θ¨=0

Differentiate radius (r) with respective to time (t).

r˙=0

Differentiate (r˙) with respective to time (t).

r¨=0

Write the expression for velocity vector (vP) of parasailer:

vP=vB+vP/B . (1)

Here, vP/B is relative velocity vector of parasailer with respect to boat.

Write the expression for acceleration vector (aP) of parasailer:

aP=aB+aP/B (2)

Here, aP/B is relative acceleration vector of parasailer with respect to boat.

Calculate the velocity vector (vP/B)radial of parasailer with respect boat using radial and transverse component:

(vP/B)radial=r˙er+rθ˙eθ

Substitute 0 for r˙, 200m for r and 2°/s for θ˙.

(vP/B)radial=0er+(200)(2°/s×πrad180°)eθ=(6.981m/s)eθ

Calculate the acceleration vector (aP/B)radial of parasailer with respect boat using radial and transverse component:

(aP/B)radial=(r¨+rθ˙2)er+(rθ¨+2r˙θ˙)eθ

Substitute 0 for r˙, 200m for r, 0 for r¨, 2°/s for θ˙, 30° for θ, and 0 for θ¨.

(aP/B)radial=(0+(200)(2°/s×πrad180°)2)er+((200)(0)+2×(0)×(0))eθ=(0.2437m/s2)er

Write the velocity vector (vP/B) of parasailer with respect boat in rectangular coordinates using Equation (1):

vP/B=(vP/B)radialsinθi+(vP/B)radialcosθj

Substitute 6.981m/s for (vP/B)radial and 30° for θ.

vP/B=6.981×sin(30°)i+6.981×cos(30°)j=3.491i+6.046j

Write the acceleration vector (aP/B) of parasailer with respect boat in rectangular coordinates using the Equation (2):

aP/B=(aP/B)radial(cosθ)i(aP/B)radialsinθj

Substitute 0.2437m/s2 for (aP/B)radial and 30° for θ.

aP/B=0.2437×(cos30°)i+0.2437×sin(30°)j=0.2111i0.1219j

Calculate the velocity vector (vP) of parasailer:

Substitute 3.491i+6.046j for vP/B and 8.333im/s for vB in Equation (1).

vP=8.333i+3.491i+6.046j=11.824i+6.046j

Here, 11.824m/s for (vp)x and 6.046m/s for (vp)y.

Calculate the velocity (vP) of parasailer using the relation:

(vp)=(vP)x2+(vP)y2

Substitute 11.824m/s for (vp)x and 6.046m/s for (vp)y.

(vp)=(11.824)2+(6.046)2=176.361=13.280m/s

Calculate the angle (α):

α=tan1((vp)y(vp)x)

Substitute 11.824m/s for (vp)x and 6.046m/s for (vp)y.

α=tan1(6.04611.824)=27.08°

Calculate the acceleration vector (aP) of parasailer:

Substitute 0.2111i0.1219j for aP/B and 0 for aB in Equation (2).

aP=0+(0.2111i0.1219j)=0.2111i0.1219j

Here, 0.2111m/s2 for (ap)x and 0.1219m/s2 for (ap)y.

Calculate the acceleration (aP) of parasailer using the relation:

(ap)=(aP)x2+(aP)y2

Substitute 0.2111m/s2 for (vp)x and 0.1219m/s2 for (vp)y.

(ap)=(0.2111)2+(0.1219)2=0.0594=0.2437m/s

Calculate the angle (ϕ):

ϕ=tan1((ap)y(ap)x)

Substitute 0.2111m/s2 for (vp)x and 0.1219m/s2 for (vp)y.

α=tan1(0.12190.2111)=30.00°

Therefore, the velocity (v) and acceleration (a) of the parasailer at this instant are 13.280m/s(27.08°)_ and 0.2437m/s(30.00°)_ respectively.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
11.163 During a parasailing ride, the boat is traveling at a constant 30 km/hr with a 200 m long tow line. At the instant shown, the angle between the line and the water is 30° and is increasing at a constant rate of 2°/s. Determine the velocity and acceleration of the parasailer at this instant.
Dynamic Question 11.81 Upon entering a curve of a 200 m radius at a speed of 72 km/h, a motorist applies his brakes to decrease his speed at a constant 2 m/s^2. Determine the magnitude of the total acceleration of the car when its speed is 54 km/h.
In 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.

Chapter 11 Solutions

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

Ch. 11.1 - The brakes of a car are applied, causing it to...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - Prob. 11.11PCh. 11.1 - Prob. 11.12PCh. 11.1 - A Scotch yoke is a mechanism that transforms the...Ch. 11.1 - For the Scotch yoke mechanism shown, the...Ch. 11.1 - Prob. 11.15PCh. 11.1 - Prob. 11.16PCh. 11.1 - Prob. 11.17PCh. 11.1 - A brass (nonmagnetic) block A and a steel magnet B...Ch. 11.1 - Based on experimental observations, the...Ch. 11.1 - A spring AB is attached to a support at A and to a...Ch. 11.1 - Prob. 11.21PCh. 11.1 - Prob. 11.22PCh. 11.1 - A ball is dropped from a boat so that it strikes...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - A human-powered vehicle (HPV) team wants to model...Ch. 11.1 - Prob. 11.27PCh. 11.1 - Based on observations, the speed of a jogger can...Ch. 11.1 - The acceleration due to gravity at an altitude y...Ch. 11.1 - The acceleration due to gravity of a particle...Ch. 11.1 - The velocity of a particle is v = v0[1 sin(t/T)]....Ch. 11.1 - An eccentric circular cam, which serves a similar...Ch. 11.2 - 11.33 An airplane begins its take-off run at A...Ch. 11.2 - Prob. 11.34PCh. 11.2 - Steep safety ramps are built beside mountain...Ch. 11.2 - A group of students launches a model rocket in the...Ch. 11.2 - A small package is released from rest at A and...Ch. 11.2 - A sprinter in a 100-m race accelerates uniformly...Ch. 11.2 - Automobile A starts from O and accelerates at the...Ch. 11.2 - In a boat race, boat A is leading boat B by 50 m...Ch. 11.2 - As relay runner A enters the 65-ft-long exchange...Ch. 11.2 - Automobiles A and B are traveling in adjacent...Ch. 11.2 - Two automobiles A and B are approaching each other...Ch. 11.2 - An elevator is moving upward at a constant speed...Ch. 11.2 - Prob. 11.45PCh. 11.2 - Prob. 11.46PCh. 11.2 - The elevator E shown in the figure moves downward...Ch. 11.2 - The elevator E shown starts from rest and moves...Ch. 11.2 - An athlete pulls handle A to the left with a...Ch. 11.2 - An athlete pulls handle A to the left with a...Ch. 11.2 - Prob. 11.51PCh. 11.2 - Prob. 11.52PCh. 11.2 - A farmer lifts his hay bales into the top loft of...Ch. 11.2 - The motor M reels in the cable at a constant rate...Ch. 11.2 - Collar A starts from rest at t = 0 and moves...Ch. 11.2 - Prob. 11.56PCh. 11.2 - Block B starts from rest, block A moves with a...Ch. 11.2 - Prob. 11.58PCh. 11.2 - The system shown starts from rest, and each...Ch. 11.2 - Prob. 11.60PCh. 11.3 - A particle moves in a straight line with a...Ch. 11.3 - Prob. 11.62PCh. 11.3 - A particle moves in a straight line with the...Ch. 11.3 - A particle moves in a straight line with the...Ch. 11.3 - A particle moves in a straight line with the...Ch. 11.3 - Prob. 11.66PCh. 11.3 - A commuter train traveling at 40 mi/h is 3 mi from...Ch. 11.3 - Prob. 11.68PCh. 11.3 - In a water-tank test involving the launching of a...Ch. 11.3 - The acceleration record shown was obtained for a...Ch. 11.3 - Prob. 11.71PCh. 11.3 - Prob. 11.72PCh. 11.3 - Prob. 11.73PCh. 11.3 - Car A is traveling on a highway at a constant...Ch. 11.3 - Prob. 11.75PCh. 11.3 - Prob. 11.76PCh. 11.3 - Prob. 11.77PCh. 11.3 - Prob. 11.78PCh. 11.3 - An airport shuttle train travels between two...Ch. 11.3 - Prob. 11.80PCh. 11.3 - Prob. 11.81PCh. 11.3 - The acceleration record shown was obtained during...Ch. 11.3 - Prob. 11.83PCh. 11.3 - Prob. 11.84PCh. 11.3 - An elevator starts from rest and rises 40 m to its...Ch. 11.3 - Two road rally checkpoints A and B are located on...Ch. 11.3 - As shown in the figure, from t = 0 to t = 4 s, the...Ch. 11.3 - Prob. 11.88PCh. 11.4 - Two model rockets are fired simultaneously from a...Ch. 11.4 - Ball A is thrown straight up. Which of the...Ch. 11.4 - Ball A is thrown straight up with an initial speed...Ch. 11.4 - Two cars are approaching an intersection at...Ch. 11.4 - Prob. 11.7CQCh. 11.4 - A ball is thrown so that the motion is defined by...Ch. 11.4 - The motion of a vibrating particle is defined by...Ch. 11.4 - Prob. 11.91PCh. 11.4 - The motion of a particle is defined by the...Ch. 11.4 - Prob. 11.93PCh. 11.4 - A girl operates a radio-controlled model car in a...Ch. 11.4 - The three-dimensional motion of a particle is...Ch. 11.4 - The three-dimensional motion of a particle is...Ch. 11.4 - Prob. 11.97PCh. 11.4 - A ski jumper starts with a horizontal take-off...Ch. 11.4 - A baseball pitching machine throws baseballs with...Ch. 11.4 - While delivering newspapers, a girl throws a...Ch. 11.4 - Prob. 11.101PCh. 11.4 - In slow pitch softball, the underhand pitch must...Ch. 11.4 - A volleyball player serves the ball with an...Ch. 11.4 - Prob. 11.104PCh. 11.4 - A homeowner uses a snowblower to clear his...Ch. 11.4 - At halftime of a football game, souvenir balls are...Ch. 11.4 - A basketball player shoots when she is 16 ft from...Ch. 11.4 - A tennis player serves the ball at a height h =...Ch. 11.4 - Prob. 11.109PCh. 11.4 - While holding one of its ends, a worker lobs a...Ch. 11.4 - Prob. 11.111PCh. 11.4 - Prob. 11.112PCh. 11.4 - Prob. 11.113PCh. 11.4 - A worker uses high-pressure water to clean the...Ch. 11.4 - An oscillating garden sprinkler which discharges...Ch. 11.4 - A nozzle at A discharges water with an initial...Ch. 11.4 - The velocities of skiers A and B are as shown....Ch. 11.4 - The three blocks shown move with constant...Ch. 11.4 - Three seconds after automobile B passes through...Ch. 11.4 - Prob. 11.120PCh. 11.4 - Airplanes A and B are flying at the same altitude...Ch. 11.4 - Prob. 11.122PCh. 11.4 - Prob. 11.123PCh. 11.4 - Prob. 11.124PCh. 11.4 - A boat is moving to the right with a constant...Ch. 11.4 - Prob. 11.126PCh. 11.4 - Prob. 11.127PCh. 11.4 - Conveyor belt A, which forms a 20 angle with the...Ch. 11.4 - During a rainstorm, the paths of the raindrops...Ch. 11.4 - Prob. 11.130PCh. 11.4 - Prob. 11.131PCh. 11.4 - As part of a department store display, a model...Ch. 11.5 - The Ferris wheel is rotating with a constant...Ch. 11.5 - Prob. 11.9CQCh. 11.5 - A child walks across merry-go-round A with a...Ch. 11.5 - Prob. 11.133PCh. 11.5 - Determine the maximum speed that the cars of the...Ch. 11.5 - Prob. 11.135PCh. 11.5 - The diameter of the eye of a stationary hurricane...Ch. 11.5 - The peripheral speed of the tooth of a...Ch. 11.5 - A robot arm moves so that P travels in a circle...Ch. 11.5 - A monorail train starts from rest on a curve of...Ch. 11.5 - Prob. 11.140PCh. 11.5 - Race car A is traveling on a straight portion of...Ch. 11.5 - At a given instant in an airplane race, airplane A...Ch. 11.5 - A race car enters the circular portion of a track...Ch. 11.5 - Prob. 11.144PCh. 11.5 - A golfer hits a golf ball from point A with an...Ch. 11.5 - Prob. 11.146PCh. 11.5 - Coal is discharged from the tailgate A of a dump...Ch. 11.5 - From measurements of a photograph, it has been...Ch. 11.5 - A child throws a ball from point A with an initial...Ch. 11.5 - A projectile is fired from point A with an initial...Ch. 11.5 - Prob. 11.151PCh. 11.5 - Prob. 11.152PCh. 11.5 - 11.153 and 11.154 A satellite will travel...Ch. 11.5 - Prob. 11.154PCh. 11.5 - Prob. 11.155PCh. 11.5 - Prob. 11.156PCh. 11.5 - Prob. 11.157PCh. 11.5 - A satellite will travel indefinitely in a circular...Ch. 11.5 - Knowing that the radius of the earth is 6370 km,...Ch. 11.5 - Satellites A and B are traveling in the same plane...Ch. 11.5 - 11.162 The path of a particle P is a limaçon. The...Ch. 11.5 - During a parasailing ride, the boat is traveling...Ch. 11.5 - Some parasailing systems use a winch to pull the...Ch. 11.5 - As rod OA rotates, pin P moves along the parabola...Ch. 11.5 - The pin at B is free to slide along the circular...Ch. 11.5 - Prob. 11.167PCh. 11.5 - After taking off, a helicopter climbs in a...Ch. 11.5 - At the bottom of a loop in the vertical plane, an...Ch. 11.5 - Prob. 11.170PCh. 11.5 - Prob. 11.171PCh. 11.5 - Prob. 11.172PCh. 11.5 - 11.173 and 11.174 A particle moves along the...Ch. 11.5 - Prob. 11.174PCh. 11.5 - Prob. 11.175PCh. 11.5 - Prob. 11.176PCh. 11.5 - Prob. 11.177PCh. 11.5 - Prob. 11.178PCh. 11.5 - Prob. 11.179PCh. 11.5 - For the conic helix of Prob. 11.95, determine the...Ch. 11 - Prob. 11.182RPCh. 11 - A drag racing car starts from rest and moves down...Ch. 11 - Prob. 11.184RPCh. 11 - The velocities of commuter trains A and B are as...Ch. 11 - Knowing that slider block A starts from rest and...Ch. 11 - Prob. 11.187RPCh. 11 - A golfer hits a ball with an initial velocity of...Ch. 11 - As the truck shown begins to back up with a...Ch. 11 - A velodrome is a specially designed track used in...Ch. 11 - Sand is discharged at A from a conveyor belt and...Ch. 11 - The end point B of a boom is originally 5 m from...Ch. 11 - A telemetry system is used to quantify kinematic...
Knowledge Booster
Background pattern image
Mechanical Engineering
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
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