Need help with escape velocity practice problem

In summary, the conversation is about finding the initial speed needed for an object launched from just above the atmosphere of Saturn to have a final speed of 28000 m/s when it is far from Saturn. The equation used for solving this problem is Vi = sqrt(Vf^2 + 2GMs(1/Δr)), where Ms is the mass of Saturn.
  • #1
MAC5494
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Homework Statement



The radius of Saturn (from the center to just above the atmosphere) is 60300 km (60300✕103 m), and its mass is 570✕1024 kg. An object is launched straight up from just above the atmosphere of Saturn.

What initial speed is needed so that when the object is far from Saturn its final speed is 28000 m/s?


Homework Equations



I'm using ΔE + ΔU = 0 and then I'm trying to derive the equation needed to solve it with the information I have. So I get Vi = sqrt(Vf^2 + 2GMs(1/Δr))

Ms = mass of saturn

The Attempt at a Solution



The answer is 45300 m/s, but I'm getting something way higher with the equation I'm using.
 
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  • #2
Just kidding. Figured it out, I messed up on the unit conversions.
 

FAQ: Need help with escape velocity practice problem

What is escape velocity?

Escape velocity is the minimum speed an object needs to achieve in order to break free from the gravitational pull of a larger object, such as a planet or moon.

How do you calculate escape velocity?

The formula for calculating escape velocity is v=sqrt((2GM)/r), where G is the gravitational constant, M is the mass of the larger object, and r is the distance between the object and the larger object.

Why is escape velocity important?

Knowing the escape velocity of a planet or moon is important for space travel and understanding the effects of gravity on objects in space. It also helps determine the minimum speed needed for a spacecraft to leave orbit and travel to other celestial bodies.

Can escape velocity vary on different planets?

Yes, escape velocity can vary on different planets due to differences in their mass and radius. For example, the escape velocity on Earth is 11.2 km/s, while on the Moon it is only 2.4 km/s.

How is escape velocity related to the mass and radius of a planet?

The escape velocity is directly proportional to the mass and inversely proportional to the radius of a planet. This means that the larger and more massive a planet is, the higher its escape velocity will be.

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