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June 2018 and 2019 Paper 1 GCE A/L Pure Mathematics with Mechanics - Introduction to GCE A/L 2019 Solution



June 2018 and 2019 Paper 1 GCE A/L Pure Mathematics with Mechanics: Introduction Topics

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  • March 14, 2021, 9:05 p.m.
    KENG ELSON MNKONG

    revise for the  mock with this question

  • Feb. 27, 2021, 9:51 a.m.
    Wanyu

    Question 12

    The horizontal distance between two men P and Q is 6 m. A ball is projected by P to Q with an initial speed of 10 ms-1. Q catches the ball at a point vertically above him and at a height 3 m above the point of projection. Show that there are two possible angles of projection  and find the time of flight in eac case (take g as 10 ms-2).

    Solution

    Diagramatic interpretation

     

       

    Showing that there are two possible angles of projection

    At point A where Q catches the ball,

    Substituting in the above equation and   we have: 

    For us to have two values of the projection angle , we must have two values for .

    For us to have two values of , the above quadratic equation in  must have two real and distinct roots. In other terms, the discriminant must be strictly positive

    Therefore, for two angles of projection  to exist, the discriminant of the above equation must be strictly positive.

    Discriminant, 

    Since , there exist two possible angles of projection.

    Finding the time of flight in each case

    The solution of the above equation in  is given by:

    Using ,

    Substituting in  above we have

    So time of flight in seconds in this case is

     

    Using ,

    Substituting in  above, we have

    So time of flight in seconds in this this case is

  • Feb. 25, 2021, 4:37 p.m.
    Kemba

    pleasw help number 13 and 12

    • Feb. 27, 2021, 7:19 a.m.
      zozo

      Helloooooooo Good morning and hope you are doing well this is really a very long question to answer here may I know exactly the difficulties you face answering the questions or if you can snap what you tried doing so that we point out the mistakes it will be great

    • Feb. 27, 2021, 9:20 a.m.
      Wanyu

      Follow the solution above

  • Feb. 23, 2021, 8:55 p.m.
    Wanyu

    Any question and submit

  • Feb. 16, 2021, 9:25 p.m.
    Phanuelex

    A smooth sphere A of mass 3m is moving with speed 5U on a smooth floor. It's collides directly with another sphere 3U. Given that the coefficient of friction is ¼ 

    Find 

    A. Velocity of the spheres after impact 

    B. The loss in K.E due to the impact

    • Feb. 17, 2021, 10:07 a.m.
      Kenyui

      actually the question lack enough information like: mass of the sphere with speed 3u was the sphere with speed 3u was moving in which direction?

  • Feb. 14, 2021, 7:48 p.m.
    Kenyui

    trig tutorials

  • Feb. 14, 2021, 7:46 p.m.
    Lynn

    A particle is projected from a poit 3h above a horizontal ground.The projection makes an angle of B with the horizontal.

    Show that if the greatest height reatched above the point of projection is h then the horizontal distance travelled before striking the horizontal ground is 6hcosB.Find the vertical component of the speed of the prticle juste before it hits the ground.

    • Feb. 14, 2021, 8:15 p.m.
      Kenyui

      use the equation of path (trajectory) or find the time taken needed to cover a vertical distance of -3h and the prove will eventually come out

    • Feb. 14, 2021, 8:15 p.m.
      Kenyui

      use the equation of path (trajectory) or find the time taken needed to cover a vertical distance of -3h and the prove will eventually come out

  • Feb. 14, 2021, 7:46 p.m.
    Kenyui

    directions

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