An asteroid with mass 250 kg is travelling directly toward the earth. When it is 25,000 km from the surface of the earth, it has a speed of 10 km/s. What is its speed when it hits the surface of the earth?
(The mass and radius of the earth are ME = 5.98 × 1024 kg and RE = 6,380 km respectively, and Newton's gravitational constant is G = 6.67300 × 10-11 m3 kg-1 s-2. You should ignore any effects due to air resistance and the rotation of the Earth)

I know the answer is 11km/s..but i cant come up with it

Question

An asteroid with mass 250 kg is travelling directly toward the earth. When it is 25,000 km from the surface of the earth, it has a speed of 10 km/s. What is its speed when it hits the surface of the earth?
(The mass and radius of the earth are ME = 5.98 × 1024 kg and RE = 6,380 km respectively, and Newton's gravitational constant is G = 6.67300 × 10-11 m3 kg-1 s-2. You should ignore any effects due to air resistance and the rotation of the Earth)

I know the answer is 11km/s..but i cant come up with it

anonymous · Answer

How do you know the answer then?

Hmm.. if in the question they give you the mass of the eart, the distance of earth and asteroid and the _gravitational_ constant... what do you think is the fundamental force this example is all about?
AAAAND for 100 points: What's the exact law regarding this particular force?

anonymous · Answer

Well so i set up kinetic and potential forces equaling each other.
The mass of the asteroid cancels out so i left it out
(.5)(10000)^2-(GM/(R+25000000))=(.5)(v^2)-(GM/R)
GM/R is basically 9.81 since it is at earth

anonymous · Answer

i converted everything to m/s because G (some sort of converter i believe) is in units that involve m not km

anonymous · Answer

just realized i wrote the wrong answer as well, its 14km/s