Escape velocity for Saturn (Introductory Mechanics)

[najatau]

Homework Statement

The radius of Saturn (from the center to just above the atmosphere) is 60,300 km (60300✕10^3 m), and its mass is 570✕10^24 kg. An object is launched straight up from just above the atmosphere of Saturn.

(a) What initial speed is needed so that when the object is far from Saturn its final speed is 17500 m/s?
My computer's answer is, "43,200 m/s"

(b) What initial speed is needed so that when the object is far from Saturn its final speed is 0 m/s? (This is called the "escape speed.")
My computer's answer is, "35,600 m/s"[/B]

Homework Equations

Energy principle

The Attempt at a Solution

For a), I get 7,747.58, which doesn't match either problem. I'm not getting b) right either.

This is a practice version of the problem, and I keep thinking I'm going about the right process for solving it, but I don't get the same answers they do, so I can't be. I've tried different variations on the energy principle:

PE (initial) - UE (initial) = PE (final) - PE (initial)

The mass of the object cancels across the equation if kinetic energy is (1/2)mv² and potential energy is (6.7x10^-11*Mm)/(r)

I thought that the way to get escape speed was sqrt(2GM/R) or sqrt((2GM/R)+v_i), but that is not working for me either. I'd really like to learn how to do these problems. I have four other similar ones that I think I'm supposed to use this same principle for, but my answers are continually wrong when I do the practice versions.

 

[ehild]

How did you get the numerical value for the speed? Did you take into account that the gravitational potential energy is negative?