/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q3.4-21E A sailboat has been running (on ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q3.4-21E (page 117)

A sailboat has been running (on a straight course) under a light wind at 1 m/sec. Suddenly the wind picks up, blowing hard enough to apply a constant force of 600 N to the sailboat. The only other force acting on the boat is water resistance that is proportional to the velocity of the boat. If the proportionality constant for water resistance is b= 100 N-sec/m and the mass of the sailboat is 50 kg, find the equation of motion of the sailboat. What is the limiting velocity of the sailboat under this wind?

Short Answer

Expert verified
  • The equation of motion of sail boat isx(t)=6t+52e-2t-52 .
  • The limiting velocity is 6 m/sec.

Step by step solution

01

Find the equation of velocity 

There are two forces are

F=600F2=-100v

Now

mdvdt=600-100v50dvdt=600-100vdvdt=12-2v鈭�dv6-v=鈭�2dt-6ln6-v=t+Cv(t)=6-Ce-2t

Put v(0) = 1 then C = 5

v(t)=6-5e-2t

02

Find the value of equation of motion

x(t)=鈭�6-5e-2tdtx(t)=6t+5e-2t2+A

When t = 0 then

x(t)=6t+5e-2t2+52

Hence, the equation of motion of sail boat is role="math" localid="1664210783875" x(t)=6t+5e-2t2+52.

The limiting velocity of the sailboat is

limv(t)t鈫�鈭�=limt鈫�鈭�(6-5e-2t)=6

Hence, the Limiting velocity is 6 m/sec.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A swimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. Starting at t = 0, city water containing 0.001% chlorine is pumped into the pool at a rate of 5 gal/min. The pool water flows out at the same rate. What is the percentage of chlorine in the pool after 1 h? When will the pool water be 0.002% chlorine?

Use the fourth-order Runge鈥揔utta subroutine with h = 0.25 to approximate the solution to the initial value problemy'=x+1-y,y(0)=1, at x = 1. Compare this approximation with the one obtained in Problem 5 using the Taylor method of order 4.

A solar hot-water-heating system consists of a hot-water tank and a solar panel. The tank is well insulated and has a time constant of 64 hr. The solar panel generates 2000 Btu/hr during the day, and the tank has a heat capacity of 2掳Fper thousand Btu. If the water in the tank is initially80掳Fand the room temperature outside the tank is, what will be the temperature in the tank after 12 hr of sunlight?

Suppose the snowball in Problem 21 melts so that the rate of change in its diameter is proportional to its surface area. Using the same given data, determine when its diameter will be 2 in. Mathematically speaking, when will the snowball disappear?

Use the improved Euler鈥檚 method with tolerance to approximate the solution to y'=1-y+y3,y(0)=0, at x= 1. For a tolerance of蔚=0.003 , use a stopping procedure based on the absolute error.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.