Having aced your introductory physics course, you are hired as a summer intern a
ID: 1396029 • Letter: H
Question
Having aced your introductory physics course, you are hired as a summer intern at NASA. You are sent as part of a team to explore the possibility of mining iron from a small, airless spherical asteroid with a radius of 534 km and a surface acceleration of 2.7 m/sec2.
1)
What is the mass of the asteroid?
kg
Your submissions:
1.15E22
Correct!
2)
What is the minimum vertical velocity you could give a 5 kg rock from the surface of this asteroid so that it continues to move upwards forever (i.e. it would never return to the surface)?
m/sec
Your submissions:
1698
Correct!
3)
What is the minimum vertical velocity you could give a 10 kg rock from the surface of this asteroid so that it continues to move upwards forever (i.e. it would never return to the surface)?
m/sec
Your submissions:
1698
Correct!
4)
How far will the 5 kg rock go if it leaves the asteroids surface with a vertical velocity of 1000 m/sec?";
m
5)
What will the speed of the 10 kg rock be at the surface of the asteroid if it is dropped from a point 1000km above the surface of the asteroid?
m/sec
I need help with questions 4 and 5! Any help will be much appreciated! Thank youy
Explanation / Answer
5) Apply enrgy conservation
initail mechaincal enrgy = final mechaincal enrgy
-G*M*m/(R+h) = -G*M*m/R + 0.5*m*v^2
0.5*m*v^2 = G*M*m/R - G*M*m/(R+h)
v = sqrt(2*G*M*(1/R - 1/(R+h))
= sqrt(2*6.67*10^-11*1.15*10^22*(1/(534*10^3) - 1/((534+1000)*10^3) )
= 1369 m/s or 1.369 km/s
follow the same procedure for 4th problem
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