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a billiard ball moving at a speed of 2.2 m/s strikes an identical stationary ball. After the collision one ball is found to be moving at a speed of 1.1 m/s in a direction making a 60 degree angle with the original line of motion. Find the velocity of the other ball if it moves off at an angle of 30 degrees.
In the direction of motion of the first ball,
Initial total momentum of the two balls is
m 2.2 kg.m/s
Final total momentum in this direction is
m v1 + m 1.1 cos 60 .
m 2.2 = m v1 + m 1.1 cos 60
2.2 = v1 cos ? + 1.1 cos 60
v1 cos ? = 1.1 cos 60 – 2.2 = -1.65
=============================
In the perpendicular direction
Initial total momentum of the two balls is 0
Final total momentum in this direction is
m v1 sin ? + m 1.1 sin 60 = 0
v1 sin ? = – 1.1 sin 60 = -0.953
========================
From the two equations
tan ? = -0.953 / -1.65 =
? = 30?
And from any one of the above equations
v1 = -1.906 m/s
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