I know that the momentum of collision before= after collision momentum

so according to that (m1xv1)+(m2xv2)=(m1+m2)v
how do i do this

v2 = 4.68*10^9 [kg]

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.

you get 2.3=1.21*\frac{a}2 or 4.6=1.21a or a=3.802 (b)

explanation: