Calculating Space Probe Speed for Escape Velocity

AI Thread Summary
To determine the speed a space probe must achieve to maintain a velocity of 3.88 km/s at an infinite distance from Earth, the concept of escape velocity is crucial. The escape velocity formula, V(escape) = √(2GM/R), indicates that a probe launched at this speed will theoretically reach infinity. However, the problem requires understanding the energy per mass of the probe and how initial velocity impacts its final speed at infinity. If the probe is projected with an initial velocity equal to the escape velocity, it will have a specific speed at infinity, which needs to be calculated to ensure it meets the 3.88 km/s requirement. Thus, the relationship between initial speed and final speed at infinity is essential for solving this problem.
kopinator
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At what speed should a space probe be fired from the Earth if it is required to still be traveling at a speed of 3.88 km/s, even after coasting to an exceedingly great distance from the planet (a distance that is essentially infinite)?

V(escape)= √(2GM/R) M= mass of Earth, R= radius of Earth

I thought this problem would have something to do with escape velocity but that doesn't seem to be right. I just don't know what to do for this problem. Any help?
 
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You can use the escape velocity as part of your solution.
It is useful to consider the energy (per mass) of the probe.
 
Do you realize that the escape velocity will take the probe to infinity?
What speed will the probe have at infinity if projected with an initial velocity equal to the escape velocity ??
 
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