Results 1 to 4 of 4

Math Help - Numerical Problem for motion along a plane (HELP)

  1. #1
    Member
    Joined
    Jan 2009
    Posts
    197

    Numerical Problem for motion along a plane (HELP)

    Question :
    A boy kicked a football with an initial velocity component of 15.0m/s and a horizontal velocity component of 22.0m/s.
    a)what is the velocity of the football(magnitude and direction)
    b)how much time is needed to reach the maximum height?

    Attempt:
    a)15m/s,N
    22.0,E
    b) no idea
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Motion of ball

    Hello mj.alawami
    Quote Originally Posted by mj.alawami View Post
    Question :
    A boy kicked a football with an initial vertical? velocity component of 15.0m/s and a horizontal velocity component of 22.0m/s.
    a)what is the velocity of the football(magnitude and direction)
    b)how much time is needed to reach the maximum height?

    Attempt:
    a)15m/s,N
    22.0,E
    b) no idea
    (a) Assuming that the 15 m/s velocity is the vertical component, the magnitude of the actual velocity is \sqrt{(15^2 + 22^2)} = 26.63 \,ms^{-1} at an angle \arctan\Big(\frac{15}{22}\Big) = 34.3^o above the horizontal.

    (b) Again, assuming that the vertical component is initially 15 m/s, the time taken to reach the maximum height is the time taken for a body to come to rest, with an initial velocity 15 m/s and an acceleration -32 m/s^2. This is \frac{15}{32} = 0.47 sec.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    644
    Hello, mj.alawami!

    A boy kicked a football with an initial vertical velocity component of 15.0 m/s
    and a horizontal velocity component of 22.0 m/s.

    a) What is the velocity of the football (magnitude and direction)?

    The velocity can be represented by this triangle:
    Code:
                          *
                      *   |
                  *       | 15
              * θ         |
          * - - - - - - - *
                 22

    The magnitude of the velocity is the length of the hyptenuse.
    . . |v| \:=\:\sqrt{22^2 + 15^2} \:=\:\sqrt{709} \:\approx\:26.6 m/s.

    The direction of the velocity is given by:
    . . \tan\theta \:=\:\frac{15}{22} \quad\Rightarrow\quad \theta \:=\:\arctan\left(\tfrac{15}{22}\right) \:\approx\:34.3^o




    b) How much time is needed to reach the maximum height?

    The height y of the football is given by: . y \:=\:15t - 4.9t^2

    The graph is a down-opening parabola which reaches its maximum at its vertex.
    The vertex is at: . t \:=\:\frac{\text{-}b}{2a} \:=\:\frac{\text{-}15}{2(\text{-}4.9)}  \:=\:1.530612245

    The ball reaches maximum height in abut 1.5 seconds.

    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Value of g

    Hello everyone -

    Thanks, Soroban. Yes, of course g = 9.8, not 32. We haven't used g = 32 in the UK for aeons, so why I used that value here I don't know.

    (Mind you, it's easier to use my method, if not my value: v = u + at \Rightarrow 0 = 15 - 9.8t \Rightarrow t \approx 1.5.)

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Motion in the xy-plane -- ahhhh
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 10th 2009, 02:11 PM
  2. Replies: 1
    Last Post: May 26th 2009, 09:41 AM
  3. Numerical Problem for motion
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 26th 2009, 01:57 AM
  4. Plane motion w/ parametric equations
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 13th 2009, 05:53 PM
  5. Motion in the xy-plane
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 13th 2008, 07:29 PM

Search Tags


/mathhelpforum @mathhelpforum