Ateam of astronauts is on a mission to land on and explore a large asteroid. in addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. with what minimum initial speed will the rocks need to be thrown in order for them never to "fall" back to the asteroid? assume that the asteroid is approximately spherical, with an average density =2.02×106 g/m3 and volume =3.09×1012 m3 . recall that the universal gravitational constant is =6.67×10−11 n·m2/kg2 .

9.60 m/s

Explanation:

The escape speed of an object from the surface of a planet/asteroid is given by:

where

G is the gravitational constant

M is the mass of the planet/asteroid

R is the radius of the planet/asteroid

In this problem we have

is the density of the asteroid

is the volume

So the mass of the asteroid is

The asteroid is approximately spherical, so its volume can be written as

where R is the radius. Solving for R,

Substituting M and R inside the formula of the escape speed, we find:

answer: 2×10^-2kg

explanation: density= mass per volume

vol=mass/density

converting to s.i units we have;

3÷1000kg = 0.003

1.5÷100m = 0.15

0.003/0.15 = 0.02kg