Jacaranda chapter 4 question

[Xandorious]

Revision question 4.7:

If a rock of mass 1kg was thrown upwards from the Earth's surface with sufficient kinetic energy to escape the EArth's gravitational field, the amount of kinetic energy required would be the area under the graph out to infinity. Using a distance of 10 Earth radii as an approximation for infinity, show that the required initial speed is 11kms^-1.

I've tried working this out, I could upload a picture of the graph but i'm not really sure how to construct this problem, (the graph is x-distance from the centre of the Earth (in Earth radii), y-gravitational field strength (Nkg^-1 or ms^-2)) I found the area of the graph from 10 earth radii but what do I do after finding the area?

EDIT: can a moderator move this to the VCE physics question thread please, thanks.

[wyzard]

Revision question 4.7:

If a rock of mass 1kg was thrown upwards from the Earth's surface with sufficient kinetic energy to escape the EArth's gravitational field, the amount of kinetic energy required would be the area under the graph out to infinity. Using a distance of 10 Earth radii as an approximation for infinity, show that the required initial speed is 11kms^-1.

I've tried working this out, I could upload a picture of the graph but i'm not really sure how to construct this problem, (the graph is x-distance from the centre of the Earth (in Earth radii), y-gravitational field strength (Nkg^-1 or ms^-2)) I found the area of the graph from 10 earth radii but what do I do after finding the area?

EDIT: can a moderator move this to the VCE physics question thread please, thanks.

The area you've found is the kinetic energy per unit mass of the object. The reason for the 'per unit mass' part is that the area under a force-distance graph represents the work done, while gravitational field strength is the force per unit mass.

Hence you'll have to convert the units in your area into SI unit, multiply it by the object's mass. That will give you the kinetic energy, which then can be used to find the velocity.