Calculate the speed of the initially stationary billiard ball after a perfectly elastic collision with an identical billiard ball. The initially moving billiard ball deflects 30.0° from its original direction while traveling at 3.00 m/s.
Calculation of Speed:
The collision between the two billiard balls is perfectly elastic, meaning that both kinetic energy and momentum are conserved during the collision. Let's denote the component of the final velocity of the initially-moving billiard ball along the direction of its original motion as x.
Since the initially moving billiard ball deflects 30.0° from its original direction, the component of velocity perpendicular to the direction of motion would be x / √3.
According to the conservation of momentum, the velocity components after the collision for the initially stationary billiard ball would be (3.00 - x) along the initial direction of motion of the incoming billiard ball, and (-x / √3) perpendicular to the direction of motion of the incoming billiard ball.
Before the collision, the kinetic energy of the incoming billiard ball would be (m/2) * (3.00)^2, where m is the mass of the billiard ball.
Using the Pythagorean Theorem for vectors, the kinetic energy of the two billiard balls after the collision can be calculated.
By simplifying the conservation of kinetic energy equation, we find that x = (9 / 4) is the valid solution for the velocity component of the initially-moving billiard ball.
Therefore, after the collision, the speed of the initially stationary billiard ball would be 1.5 m/s.