Answer:
v2 = 4.68*10^9 [kg]
Step-by-step explanation:
In this problem we must show that the speed the mass of the asteroid is approximately equal to that mentioned in numeral a).
We need to identify the initial data.
m1 = 300 [kg] (mass of the dart)
v1 = 6250 [m/s]
v2 = 0.4 [mm/s] = 0.0004[m/s]
Using the equation for this type of collision
(m1*v1) + (m2*v2) = (m1+m2)*v2
Now the key to solving this problem is the term relative speed, relative speed is defined as the speed of one body relative to the other in a given instant. For this case it has a relative speed of 6250 [m/s] of the Dart with respect to the asteroid before impact, so the speed of the asteroid before impact is taken as zero.
Therefore:
(m1*v1) = (m1+m2)*v2
(300*6250) = (300*0.0004) + 0.0004*v2
v2 = 4.68*10^9 [kg]
This is approximately equal to the value of point a.