Deriving Projectile Motion Equations

  1. 1. The problem statement, all variables and given/known data

    A projectile is fired from ground level at time t=0, at an angle of θ with respect to the horizontal. It has initial speed V0.

    Part A

    Find the time it takes the projectile to reach its maximum height. Express in terms of V0, θ, and g.

    Part B

    Find the time at which the projectile hits the ground after having traveled through a horizontal distance, R. Express in terms of V0, θ, and g.

    Part C

    Find the maximum height attained by the projectile. Express in terms of V0, θ, and g.

    Part D

    Find the total distance R traveled in the x direction. Express in terms of V0, θ, and g.


    2. Relevant equations

    V=V0+at

    y=y0+Vy0t+0.5ayt2

    x=Vx0t

    3. The attempt at a solution

    For Part A, I did:

    Vy=Vy0 + ayt

    0=V0sinθ-gt

    gt=V0sinθ

    t=(V0sinθ)/g

    For Part B I did:

    y=y0+Vy0+0.5ayt2

    0=0 + (V0sinθ)t- 0.5gt2

    0.5gt2=(V0sinθ)t

    gt2= (2V0sinθ)t

    t= (2V0sinθ)/g

    For Part C I did:

    Vy2=Vy02+2ay

    0=(V0sinθ)2-2gy

    y= (V0sinθ)2/2g

    For Part D:

    x = x0 + Vx0t

    x= V0cosθ × (2V0sinθ)/g

    x= (V02sin2θ)/g

    Did I do this correctly?? Or did I just mess up everything.. The one I'm really confused about is Part C.. I don't know if I could use the equation that I used..
     
  2. jcsd
  3. haruspex

    haruspex 14,355
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    All good.
     
  4. Really!? So I am right.. I was told by someone that part C was wrong.. o_o
     
  5. haruspex

    haruspex 14,355
    Science Advisor
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    Checked it again... part C still looks right to me.
     
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