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March 2, 2015

March 2, 2015

Posted by **Anna** on Thursday, June 28, 2012 at 8:48pm.

(a) Use these numbers to calculate the escape speed from the surface of Eris.

(b) If an object is fired directly upward from the surface of Eris with half of this escape speed, to what maximum height above the surface will the object rise? (Assume that Eris has no atmosphere and negligible rotation.)

I know the speed is 1360 m/s but how do you solve question b? The answer is 400 km. Thank you in advance.

- Physics -
**ajayb**, Friday, June 29, 2012 at 3:08pmA)

Escape vel. = Ue = sqrt(2GM/R) ...(1)

also g = GM/R^2 So GM/R = gR .....(2)

From(1) & (2)

Ue = sqrt(2gR) = sqrt(2*0.77*1200,000)

= 1360 m/s

B)

u = Ue/2 = (1/2)*sqrt(2GM/R)

Now KEi+PEi = PEf+KEf (conservation of mechanical energy)

or (1/2)mu^2 - GMm/R = -GMm/(R+h)+0

or GM/4R - GM/R = -GM/(R+h)

or 3/4R = 1/(R+h)

or h = R/3 = 400 Km

- Physics -
**Anna**, Sunday, July 1, 2012 at 12:06amI'm having trouble following this. How do you go from:

GM/4R - GM/R = -GM/(R + h) to 3/4R = 1/(R+h) to

h=R/3?

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