Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    12
    ReputationRep:
    Each of two forces has magnitude X N, and the resultant of the two forces has magnitude 12N. When the magnitude of one of the forces is increased by 70% the magnitude of the resultant of the two forces becomes 21N. Find X and the angle between the two forces

    I know in the second one. One must use 1.7x.

    However, still not sure about how to go about it. Help would be appreciated.
    Offline

    14
    ReputationRep:
    Are you provided with a diagram?
    • Thread Starter
    Offline

    12
    ReputationRep:
    Nope.
    Offline

    14
    ReputationRep:
    (Original post by Deep456)
    Nope.
    It's a puzzle. Have you typed the question EXACTLY as printed. If not can you give the exact wording?
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by steve2005)
    It's a puzzle. Have you typed the question EXACTLY as printed. If not can you give the exact wording?
    Well it's from a friend of mine and he says he gave it exactly as it is written.

    We have both establised:

    12² = X² + X² + 2XXcos(theta) = 2X²(1+2cos(theta))

    21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

    Now how to solve?
    Offline

    14
    ReputationRep:
    I think these are the diagrams. The angle theta is NOT the required angle but when you know this it is easy to get the required angle.

    Offline

    14
    ReputationRep:
    (Original post by Deep456)
    Well it's from a friend of mine and he says he gave it exactly as it is written.

    We have both establised:

    12² = X² + X² + 2XXcos(theta) = 2X²(1+2cos(theta))

    21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

    Now how to solve?
    Make \cos\theta the subject of both equations and then solve for X then find angle.
    Offline

    14
    ReputationRep:
    (Original post by Deep456)
    Well it's from a friend of mine and he says he gave it exactly as it is written.

    We have both establised:

    12² = X² + X² + 2XXcos(theta) = 2X²(1+2cos(theta))

    21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

    Now how to solve?
    21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

    The bold should be 3.89X²
    • Study Helper
    Offline

    13
    Study Helper
    (Original post by Deep456)
    Now how to solve?
    I'm inclined to make the entire "x^2Cos(theta)" term the subject of each, equate the two, and solve the quadratic for "x".
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Has a teacher ever helped you cheat?
    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

    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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.