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Deriving Projectile Motion Equations 
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#1
Jun313, 10:50 PM

P: 64

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 V_{0}. Part A Find the time it takes the projectile to reach its maximum height. Express in terms of V_{0}, 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 V_{0}, θ, and g. Part C Find the maximum height attained by the projectile. Express in terms of V_{0}, θ, and g. Part D Find the total distance R traveled in the x direction. Express in terms of V_{0}, θ, and g. 2. Relevant equations V=V_{0}+at y=y_{0}+V_{y0}t+0.5a_{y}t^{2} x=V_{x0}t 3. The attempt at a solution For Part A, I did: V_{y}=V_{y0} + a_{y}t 0=V_{0}sinθgt gt=V_{0}sinθ t=(V_{0}sinθ)/g For Part B I did: y=y_{0}+V_{y0}+0.5a_{y}t^{2} 0=0 + (V_{0}sinθ)t 0.5gt^{2} 0.5gt^{2}=(V_{0}sinθ)t gt^{2}= (2V_{0}sinθ)t t= (2V_{0}sinθ)/g For Part C I did: Vy^{2}=Vy0^{2}+2ay 0=(V_{0}sinθ)^{2}2gy y= (V_{0}sinθ)^{2}/2g For Part D: x = x_{0} + V_{x0}t x= V_{0}cosθ × (2V_{0}sinθ)/g x= (V0^{2}sin2θ)/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
Jun313, 11:49 PM

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All good.



#3
Jun413, 07:33 AM

P: 64

Really!? So I am right.. I was told by someone that part C was wrong.. o_o



#4
Jun413, 04:37 PM

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Deriving Projectile Motion Equations
Checked it again... part C still looks right to me.



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