Escape velocity of rocket determination problem

[discusslife]

if you want to know escape velocity ok? it is the minimum velocity ok? required by the body or satelite ok? to escape the earth's graviational pull ok? to the inifinity ok?

[XanCharb]

So the energy required is Integral(g*m*(yo/yf)^2*dyf) as yf goes from yo to infinity. = g*m*yo^2*Integral(yf^-2*dyf) = g*m*yo^2*(-1/yf) = g*m*yo^2*(0 - (-1/yo)) = g*m*yo g*m*yo = 1/2*m*v^2 g*yo = 1/2*v^2 v = sqrt(2*g*yo) v = sqrt(2*32ft/s/s*4000mi) v = sqrt(2*32ft/s/s*1mi/5280ft*400­0mi) v = sqrt(48.48*(mi^2)/(s^2)) v = 6.96 mi/s

[airpower123]

omg ur so powerfull. what u gonna do? break me down to the lowest common denminator. then intergrate my face? iam gonna diffentiate u to the floor.

[XanCharb]

You don't need the mass of the Earth if you know the acceleration due to gravity at a point, as we know on the surface it's 32ft/s^2.

yo (y initial - that's ugly) = radius of the earth

yf (y final - ugly again) = new height (from the center)

The energy to lift an object a small distance, dyf, is g*m*(yo/yf)^2*dyf, in other words, the weight of the object times the square of the ratio of the initial height to the final height.

[GoddnRunn]

Yes and how do we know what g is ? Its G*M/R^2 where M is the mass of the earth and R is the radius of the earth. We were given R; G is a formulaic constant and M is unknown. We were not given g. Sure - if we could make assumptions, we could pull either g or M out of our asses.

[GoddnRunn]

If we could just pull non-formulaic constants out of our ass, why not the escape velocity itself?

[marjan15]

It's about 11.2 km/s for objects without engines or any kind of energy source with them.

For real life rockets it's about 20 m/s and then faster and faster. :)

[GoddnRunn]

You need to know the average density of the Earth.

[mathproblems]

why?

[GoddnRunn]

Because the gravitational force acting on the rocket is proportional to the mass of the earth. (F = G*m1*m2/d^2)