# Deriving Projectile Motion Equations

by rakeru
Tags: deriving, equations, motion, projectile
 P: 60 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..
 Homework Sci Advisor HW Helper Thanks P: 8,912 All good.
 P: 60 Really!? So I am right.. I was told by someone that part C was wrong.. o_o
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