Question

Two billiard balls are rolling on a flat table and have velocity component (1 ms^-1, √3 ms^-1) and (2 ms^-1, 2 ms^-1) respectively, If both the balls start moving from the same point, what is the angle between their paths?

Answer 1

For the first ball

OC = v_x = 1 ms^-1,

OE = v_y = √3 ms^-1

Resultant of v_x and v_y is given by OA

OA = √(v_x² + v_y²) = √(1 + 3) = 2 ms^-1

Let the resultant makes an angle α with x-axis

Resultant of v'_x and v'_y is given by OB

Let the resultant makes an angle α' with x-axis.

Thus, tan α' = BD/OD = 2/2 = 1 or, α' = 45°

The angle between the paths of two balls

 α' -  α' = 60°- 45° = 15°.