Observations of galaxies and clusters of galaxies indicate that about ____ percent of the matter in the universe is dark matter.
1 answer:
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Answer:
The final speed for the mass 2m is and the final speed for the mass 9m is
.
The angle at which the particle 9m is scattered is with respect to the - y axis.
Explanation:
In an elastic collision the total linear momentum and the total kinetic energy is conserved.
<u>Conservation of linear momentum:</u>
Because the linear momentum is a vector quantity we consider the conservation of the components of momentum in the x and y axis.
The subindex 1 will refer to the particle 9m and the subindex 2 will refer to the particle 2m
In the x axis before the collision we have
and after the collision we have that
In the y axis before the collision
after the collision we have that
so
then
<u>Conservation of kinetic energy:</u>
so
Putting in one side of the equation each speed we get
We know that the particle 2m travels in the -y axis because it was stated in the question.
Now we can get the y component of the speed of the 9m particle:
the magnitude of the final speed of the particle 9m is
The tangent that the speed of the particle 9m makes with the -y axis is
As a vector the speed of the particle 9m is:
As a vector the speed of the particle 2m is: