Universal Gravitation on escape velocity

[tubworld]

On dealing with Universal Gravitation topic, I came across this question:
what is the min speed, relative to the sun, necessary for a spacecraft to escape the solar system if it starts at the Earth's orbit?

My working:

v=sqrt(2GM/R), where G=universal constant, R= distance between Earth and sun and m= mass of sun. Is that all?

The second part of it states that a spaceship achieved a max speed of 125000km/h on its way to photograph jupiter. Beyond what distance from the sun is this speed sufficient to escape the solar system?

for the second part, any hints? I am getting stuck. Do i need to know the order of the planets for the second part?

 

[tubworld]

add on my 2 cents worth

Something just came to me: for part a do i need to consider the escape speed to leave the Earth as well. (i.e. escape speed to leave Earth + escape speed to leave sun)?

 

[Janus]

On dealing with Universal Gravitation topic, I came across this question:
what is the min speed, relative to the sun, necessary for a spacecraft to escape the solar system if it starts at the Earth's orbit?
My working:
v=sqrt(2GM/R), where G=universal constant, R= distance between Earth and sun and m= mass of sun. Is that all?
The second part of it states that a spaceship achieved a max speed of 125000km/h on its way to photograph jupiter. Beyond what distance from the sun is this speed sufficient to escape the solar system?
for the second part, any hints? I am getting stuck. Do i need to know the order of the planets for the second part?

As for the first part, if your spacecraft is moving in Earth's orbit around the Sun it already has some orbital velocity and you need to take this into account when calculating how much additional velocity is needed to reach solar escape velocity. I would not worry about earrh escape velocity as the problem does not say that you are starting on the surface of the Earth.

For the second part, try re-arranging your formula so that it solves for R rather than V.