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Projectile motion of a ball

  1. Apr 24, 2014 #1
    1. The problem statement, all variables and given/known data

    This is a review question from the test I did few months back, and I need to review it for my finals.

    A ball is thrown from the top of a building 35m high with an initial speed of Vi at an angle 30° above the horizontal. The ball strikes the ground at a point 80m from the base of the building. Find

    a) the time of the ball is in the flight
    b) the horizontal and vertical component of the initial velocity
    c) its initial velocity and
    d) the velocity of the ball just before it strikes the ground


    2. Relevant equations

    Sy= Viy t + 1/2Ayt^2

    3. The attempt at a solution

    My attempt was resolving into x and y direction, so,

    Ax= 0 Ay=-9.8m/s
    Sx= 80m Sy=-35, Viy= 0

    Therefore: Sy= Viy+1/2Ayt^2
    -35= 0 + 1/2(-9.8)t^2
    Finally: My t = 2.67s

    Apparently, I was marked wrong, so my time I found is wrong and therefore I couldn't proceed with b,c and d with the wrong time.

    Help would be really appreciated! Thanks.
     
  2. jcsd
  3. Apr 24, 2014 #2

    SteamKing

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    The problem clearly states that the ball is thrown at initial speed Vi at an angle of 30 degrees above the horizontal.

    Why did you take Viy = 0? When is Viy = 0 during the flight of the ball?
     
  4. Apr 24, 2014 #3
    Oh, I think I figured it out

    So its, I use Vx = Vicos30°
    V = s/t
    V = 80 / t cos30°

    Then with this equation V = 80 / t Vicos30° I sub into my component y which is
    -35 = Vi sin30 t-4.9t^2
    -35 = 80 sin30 t/ t cos30° - 4.9t^2
    t = 4.07s

    Is it right?
     
  5. Apr 24, 2014 #4

    SteamKing

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    I don't know why you are using V = s/t here. The initial velocity Vi is a given.

    The path of the ball is analyzed in two parts: the first part is the ball travelling upward until gravity reduces the vertical velocity to zero. The second part starts at this point as the ball free falls from the apex of its trajectory and hits the ground.

    A simple sketch would be most helpful in analyzing this type of problem, rather than just throwing a bunch of random formulas at it.
     
  6. Apr 24, 2014 #5
    For my vertical component, its -35 = Vi sin30 t -4.9t^2
    At this stage, how am I going to solve with Vi being an unknown instead of a value?
     
  7. Apr 24, 2014 #6

    SteamKing

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    Vertical component of what? The 35 m building is just sitting there.

    You'll have to solve for time in terms of Vi, since a numerical value is not disclosed.
     
  8. Apr 27, 2014 #7
    After thinking real hard for almost 2 days.

    I know that my horizontal and vertical component has the same time is in flight. So I can use resolve my t initially in the horizontal component of the flight using Sx = Vicos30 t right. So wouldn't be
    t = Sx / Vi cos 30

    Knowing my Sx is 80 and cos 30 is 0.87
    Hence t = 92.38 / Vi
    The problem is I can't eliminate my Vi. So like you said.. I treat my time in terms of Vi. Therefore my answer is t = 92.38 / Vi ??
     
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