In a pool game, the cue ball, which has an initial speed of 9 m/s, makes an elas

Question

In a pool game, the cue ball, which has an initial speed of 9 m/s, makes an elastic collision with the eight ball, which is initially at rest. The two balls have equal masses of 2 kg. After the collision, the eight ball moves at an an angle of 45.7 ? to the original direction of the cue ball.

What angle does the cue ball make with respect to the original line of motion? Answer in units of ? .

(ii) Find the speed of the cue ball. Answer in units of m/s.

(iii) Find the speed of the eight ball. Answer in units of m/s.

Explanation / Answer

Using Momentum Conservation,
In X Direction,
m*9 = m*v1*cos(1) + m*v2*cos(45.7)
9 = v1*cos(1) + v2*cos(45.7)
v1*cos(1) = 9 - 0.698 v2   -------1

In Y Direction,
m*v1*sin(1) = m*v2*sin(45.7)
v1*sin(1) = v2*sin(45.7) -------------2

Squaring and adding 1 & 2,
v1^2 = (9 - 0.698*v2)^2 + (0.715*v2)^2 ---------3

As Collision is Elastic K.E is conserved.
Using Energy Conservation,
1/2*m*v^2 = 1/2*m*v1^2 + 1/2*m*v2^2
9^2 = v1^2 + v2^2 ------------4

Solving eq 3 & 4,

v1 = 6.44 m/s
v2 = 6.29 m/s

Substituing value in eq 2
6.44*sin(1) = 6.29*sin(45.7)
1 = sin^-1((6.29*sin(45.7 degree)) / 6.44)
1 = 44.35o

(i) What angle does the cue ball make with respect to the original line of motion? 1 = 44.35o.

(ii) Find the speed of the cue ball, 6.44 m/s

(iii) Find the speed of the eight ball, 6.29 m/s

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