Question #89599
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.
1
Expert's answer
2019-05-15T10:15:39-0400

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


mvm+MvMcosα=(m+M)Vcosβm*vm+M*vM*cos\alpha=(m+M)*V*cos\beta

Oy


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

V- velocity after collide.

The result is the following system


Vcosβ=7vm/16V*cos\beta=7*vm/16

Vsinβ=33vm/8V*sin\beta=3*\sqrt{3}*vm/8

Solving it we get


V=0.78vmV=0.78*vm

β=56\beta=56


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