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CubeDude
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Homework Statement
A Rocket is initially at rest on the ground. The rocket flies off in a straight line at an angle 53.1 degrees above the horizontal with a constant acceleration of magnitude [tex]\textbf{g}[/tex]. The engines stop at a time [tex]\textbf{T}[/tex] after launch, after which the rocket is in projectile motion.
Ignoring air resistance, and assuming [tex]\textbf{g}[/tex] is indepedent of altitude; Find the maximum altitude reached by the rocket, your answer should be in terms of [tex]\textbf{g}[/tex] and [tex]\textbf{T}[/tex].
Homework Equations
y = y0 + V0yt + [tex]1/2[/tex]at[tex]^{2}[/tex]
V22 = V12 + 2aY
V1 = V0 + at
The Attempt at a Solution
]I attempt to tackle this problem by seperately finding an expression for height after time [tex]\textbf{T}[/tex], and an expression for the maximum height of a projectile released with the velocity the rocket has at time [tex]\textbf{T}[/tex]. I would then take the maximum height to be the sum of these two expressions.
The question states that the rocket travels in a straight line. Am I right to assume that this means before time [tex]\textbf{T}[/tex] the vertical component of the rocket's acceleration is equal to the acceleration due to gravity but in the oposite direction?
If I assume the acceleration before time [tex]\textbf{T}[/tex] is zero, then the height reached by the rocket at time [tex]\textbf{T}[/tex] is given by:
y1 = (V0Sin[tex]\alpha[/tex])[tex]\textbf{T}[/tex]
If the rocket is not accelerating then at time [tex]\textbf{T}[/tex] the velocity will be equal to the rocket's intitial velocity.
Using:
V22 = V12 + 2aY2
Taking V22 = 0, and rearranging.
Y2 = (V02Sin2[tex]\alpha[/tex]) [tex]1/2g[/tex]
The correct answer is independent of the Rocket's initial velocity. I don't see how I can cancel these out, so I must be going wrong somewhere.
I don't start my Physics course until October, but I'm trying to get a bit of a head start and this is the first problem I've become stuck on. Any hints to nudge me in the right direction would be greatly appreciated.
(I can't seem to make the alpha next to the Sin stay at the same level as the Sin. It should mean Sin of the angle alpha.)
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