Answer to Question #89599 in Astronomy | Astrophysics for sathwik

Question

A warning system has calculated that two asteroids will collide not far from Earth any time soon.
The smaller asteroid has the mass m and moves with the velocity vm. The bigger asteroid has the
mass M = 3m and the velocity of vM =
1
2
vm. They collide at an angle of α = 60◦ and turn into a
single heavy asteroid (inelastic collision):
M
m
α
β
(a) Calculate the velocity of the single object aer the collision.
(b) Determine the angle β aer the collision.

Answer 1

We direct the axis ox along the motion of the asteroid with a smaller mass m, and oy - perpendicular to it.

Then the law of conservation of momentum on the axis:

Ox

$$m*vm+M*vM*cos\alpha=(m+M)*V*cos\beta$$

Oy

$$M*vM*sin\alpha=(m+M)*V*sin\beta$$

V- velocity after collide.

The result is the following system

$$V*cos\beta=7*vm/16$$

$$V*sin\beta=3*\sqrt{3}*vm/8$$

Solving it we get

$$V=0.78*vm$$

$$\beta=56$$