Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    hey could you give me a hand with this please....Im rather stuck


    a boat sails across a straight river, of uniform width W, starting from point O
    on one bank of the river. the velocity of the river at a distance Y from the bank is u(y)=ay(W-y)
    where a is a positive constant, the boat travels at a constant speed V relative to the current and steers a course set at a constant angle S where (0<s<pi) to the downstream direction.

    a) show that the velocity of the boat relative to a cartesian coordiante system with origin at O and i pointing in the downward direction and j pointing across
    (u+vcosS)i+(vsinS)j

    b) at what time does the boat reach the other bank
    c) show what when the boat has reached the other bank the downsteram distance it has travelled is equal to
    aW³ ÷ 6vsinS + WcotS


    thanks!
    Offline

    0
    ReputationRep:
    number one, sketch a picture :rolleyes: that really makes the difference.
    part a) is resolving into components, in the i direction there is the added speed of the water.

    b) time = distance/speed, just got to consider the component of velocity

    c) once you find time t, you can find downstream distance by using distance = speed*time (same time that you calculated), the speed is the component of velocity in that direction. It means you get an expression almost at the final answer except there is a u(y)
    it is found by integration with respect to y, the limits are from y = 0 to y = , I'll let you consider the upper limit.

    hope it works out ok.

    (correction, there seems like an extra factor of W in the integral term when you work it out, I'm not entirely sure about it, may be in doing the integration you got to multiply by a factor of 1/W so that you are essentially taking the average speed, if you don't multiply by 1/W I'm not sure if it works, it may not be the right method but it's a way)
    Offline

    2
    ReputationRep:
    (Original post by apple tree)
    number one, sketch a picture :rolleyes: that really makes the difference.
    part a) is resolving into components, in the i direction there is the added speed of the water.

    b) time = distance/speed, just got to consider the component of velocity

    c) once you find time t, you can find downstream distance by using distance = speed*time (same time that you calculated), the speed is the component of velocity in that direction. It means you get an expression almost at the final answer except there is a u(y)
    it is found by integration with respect to y, the limits are from y = 0 to y = , I'll let you consider the upper limit.

    hope it works out ok.
    Hey I'm not entirely sure if I follow your method. How do I resolve into components?
    (correction, there seems like an extra factor of W in the integral term when you work it out, I'm not entirely sure about it, may be in doing the integration you got to multiply by a factor of 1/W so that you are essentially taking the average speed, if you don't multiply by 1/W I'm not sure if it works, it may not be the right method but it's a way)
    I'm not entirely sure if i follow your method, how would you resolve into components?
 
 
 

University open days

  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
  • Heriot-Watt University
    All Schools Postgraduate
    Wed, 21 Nov '18
Poll
Black Friday: Yay or Nay?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.