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2D Projectile Motion - Minimum Speed

  1. Oct 10, 2008 #1
    1. The problem statement, all variables and given/known data
    Salmon often jum waterfalls to reach their breeding grounds.
    The acceleration of gravity is 9.81 m/s^2
    Starting 1.73 m from a waterfall .0386 m in height, at what minimum speed must a salmon jumping at an angle of 44.3 degrees leave the water to continue upstream? Answer in units of m/s.

    2. Relevant equations
    Vox = Vocos(theta)
    Vox = 6.179cos(44.3) = 4.42
    Voy = Vosin(theta)
    Voy = 6.179sin(44.3) = 4.316


    3. The attempt at a solution
    - I drew a graph:
    x-axis labeled as 1.73m and the y-axis labeled as .386m

    - Tried to find time:
    t = (sqrt) 2(h)/g
    t = (sqrt) 2(.386)/9.81
    t = .28 seconds <-- I think this may be wrong.

    - Tried to find Vo:
    Vo = x/t
    Vo = 1.73/.28
    Vo = 6.179

    Now plugged Vo result to find components:
    Vox = Vocos(theta)
    Vox = (6.179)cos(44.3)
    Vox = 4.42

    Voy = Vosin(theta)
    Voy = (6.179)sin(44.3)
    Voy = 4.316

    ... I'm not sure what to do next. Am I supposed to use the Pythagorean Theorem? And find the tangent? I have no clue. All help would be appreciated. =)
     
  2. jcsd
  3. Oct 10, 2008 #2
    I am sorry to ask this, but are you sure you did actually read the problem?
    You have to FIND the initial velocity, it is not give.
    The angle is given, so you don't need to find it (by using tangent...).
    Where did you get the value of 6.179 from?

    "t = (sqrt) 2(h)/g
    t = (sqrt) 2(.386)/9.81
    t = .28 seconds <-- I think this may be wrong."

    You are right (that it is wrong). The vertical motion has initial speed (voy):
    y=voy*t-1/2*g*t^2

    What yo have to do is to write equations of motion for both x and y direction and solve them to find vox and voy.
    Hint: you can start by finding what is voy in order to reach the given height.
     
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