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Deriving Projectile Motion Equations

by rakeru
Tags: deriving, equations, motion, projectile
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rakeru
#1
Jun3-13, 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 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..
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haruspex
#2
Jun3-13, 11:49 PM
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All good.
rakeru
#3
Jun4-13, 07:33 AM
P: 64
Really!? So I am right.. I was told by someone that part C was wrong.. o_o

haruspex
#4
Jun4-13, 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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