Question

Two identical spherical asteroids (mass 3.07x10^{18} kg,
radius 5.5x10^{3} m) are initially at rest, with their
centers 6.01x10^{5} m apart. Ignore all other objects in
the universe, and friction. The two asteroids accelerate toward
each other, due to gravity, until they finally crash together. At
what speed, in m/s, will each asteroid be moving when they collide
(just touch on their outer edge)?

** NOTE**: when the asteroids collide, the
distance between the centers of the asteroids is

Answer #1

**let
m = 3.07*10^18 kg
r = 5.5*10^3 m**

**initial distance between the asteroids, d1 = 6.01*10^5
m
final distance between the asteroids, d2 = 2*r**

**= 2*5.5*10^3**

**= 1.10*10^4 m**

**let v is the speed of asteroids when they
collide.**

**Apply conservation of energy**

**KEf + PEf = KEi + PEi**

**2*(1/2)*m*v^2 - G*m^2/d2 = 0 - G*m^2/d1**

**m*v^2 = G*m^2*(1/d2 - 1/d1)**

**v^2 = G*m*(1/d2 - 1/d1)**

**v = sqrt(G*m*(1/d2 - 1/d1) )**

**= sqrt(6.67*10^-11*3.07*10^18*(1/(1.1*10^4) -
1/(6.01*10^5))**

**= 135 m/s
<<<<<<<<<<----------------------Answer**

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