In a game of pool, the cue ball strikes another ball initially at rest. After the collision, the cue ball moves at 4.15 m/s along a line making an angle of -25° (i.e. below the x-axis) with its original direction of motion (the x-axis), and the second ball has a speed of 2.846 m/s.

Question

In a game of pool, the cue ball strikes another ball initially at rest. After the collision, the cue ball moves at 4.15 m/s along a line making an angle of -25° (i.e. below the x-axis) with its original direction of motion (the x-axis), and the second ball has a speed of 2.846 m/s. 
Find the angle between the direction of motion of the second ball and the original direction of motion of the cue ball. Assume the masses are equal.

Find the original speed of the cue ball.

Is kinetic energy conserved?

Elena · Accepted Answer

According to the law of conservation of linear momentum
vector(p)= vector(p1)+ vector(p2),
Let vector( p) is directed along +x-axis. Then vector (p1) is
below x-axis and vector(p2) is above it.
Projections on axes are
x: v = v1•cosα +v2•cosβ
y: 0 = - v1•sin α +v2•sinβ
sinβ = v1•sin α/v2 = 0.616.
β = arcsin 0.616 = 38 degr.
cos β = 0.788.
v = 4.15•0.906+2.846•0.788=6 m/s.
At elastic collision the kinetic energy is conserved.