- #1
JFonseka
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Homework Statement
A projectile is launched from the surface of a planet (mass = M, radius = R). What minimum launch speed is required if the projectile is to rise to a height of 2R above the surface of the planet? Disregard any dissipative effects of the atmosphere.
Homework Equations
v = [tex]\sqrt{2GM/R}[/tex]
The Attempt at a Solution
So we know that for a projectile to rise to a height of R above the planet, the equation above will suffice, however the projectile in this question has to rise to a height of 2R, that is R + 2R, so 3R. I thought you simply replace R by 3R, to get v = [tex]\sqrt{2GM/3R}[/tex]
But that's not the case, the multiple choices does not have that as one of the answers. The answers listed were...
a) [tex]\sqrt{\frac{4GM}{3R}}[/tex]
b) [tex]\sqrt{\frac{8GM}{5R}}[/tex]
c) [tex]\sqrt{\frac{3GM}{2R}}[/tex]
d) [tex]\sqrt{\frac{5GM}{3R}}[/tex]
e) [tex]\sqrt{\frac{GM}{3R}}[/tex]
I think the most sensible looks to be GM/3R but I'm probably wrong, how should I go about doing this problem?
Thanks