(III) Billiard balls A and B, of equal mass, move at right angles and meet at the origin of an xy coordinate system as shown in Fig. 7-36. Initially ball A is moving along the y axis at +2.0 m/s, and ball B is moving to the right along the x axis with speed +3.7 m/s. After the collision (assumed elastic), ball B is moving along the positive y axis (Fig. 7-36) with velocity v'B. What is the final direction of ball A, and what are the speeds of the two balls?
FIGURE 7;36 Problem 46. (Ball A after the collision is not shown.)
Whenever two bodies collide, their speed and direction of motion changes. In this problem, we have to determine speed of ball A and ball B, and the final direction of ball A after collision.
Step 1 of 5</p>
Law of conservation of linear momentum: When no external force acts on the system, then the final momentum of the system is equal to their initial momentum.
Law of conservation of Energy: Energy can neither be created nor be destroyed. It can only be converted from one form into other. The total amount of energy in an isolated system remains constant.
Step 2 of 5</p>
Let the mass of balls be
The initial speed of balls A and B are and respectively.
The final speed of ball B is along positive y-axis.
Let the final speed of ball A be making an angle with the positive x-axis as shown in figure below.
Step 3 of 5</p>
As no external force acts on the system, therefore momentum has to conserved.
Applying law of conservation of momentum along x-axis, we get,
Similarly, applying law of conservation of momentum along y-axis, we get,
Squaring and adding equations (1) and (2), we get,