# Space Probe speed

1. Apr 1, 2013

### kopinator

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?

2. Apr 1, 2013

### Staff: Mentor

You can use the escape velocity as part of your solution.
It is useful to consider the energy (per mass) of the probe.

3. Apr 1, 2013

### technician

Do you realise 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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