When a cue ball strikes another ball, what is the largest possible angle the struck ball can be deflected from the line along which the cue ball was travelling?
I'd have to say 90 degrees. If the struck ball has some backward velocity, the striking ball would have to increase its forward speed to compensate.
The largest possible angle the struck ball can be deflected from the line along which the cue ball was traveling depends on various factors, including the speed and angle of the cue ball's initial impact, the type and condition of the balls, and the table's playing surface. To determine the maximum angle of deflection, you can consider the principles of physics, specifically the law of conservation of momentum and the angles of incidence and reflection.
1. Law of Conservation of Momentum: When two objects collide, the total momentum before the collision is equal to the total momentum after the collision. In this case, the initial momentum of the cue ball before collision should be equal to the combined momentum of the cue ball and the struck ball after collision.
2. Angles of Incidence and Reflection: The angle at which the cue ball strikes the struck ball is called the angle of incidence, and the angle at which the struck ball changes direction is called the angle of reflection. According to the law of reflection, the angle of incidence is equal to the angle of reflection.
To calculate the maximum angle of deflection, you would need to consider the specific values for these variables, such as the masses and velocities of the balls, as well as the angles at which they collide. A more accurate analysis can be performed using mathematical equations and the principles of conservation of momentum and energy.
Therefore, without specific values for the variables involved, it is not possible to determine the largest possible angle of deflection accurately.