A billiard ball traveling at 3.00 m/s collides perfectly elastically with an identical billiard ball initially at rest on the level table. The initially moving billiard ball deflects 30.0° from its original direction. What is the speed of the initially stationary billiard ball after the collision?

3sin(30)=1.5

To find the speed of the initially stationary billiard ball after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.

First, let's label the initial ball as ball 1 and the stationary ball as ball 2.

Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision:

m1v1i + m2v2i = m1v1f + m2v2f

Where:
m1 = mass of ball 1
m2 = mass of ball 2
v1i = initial velocity of ball 1
v2i = initial velocity of ball 2
v1f = final velocity of ball 1
v2f = final velocity of ball 2

In this case, since the balls are identical, their masses are equal and can be represented by 'm':

m * v1i + m * 0 = m * v1f + m * v2f

Since the second ball is stationary initially (v2i = 0), the equation simplifies to:

v1i = v1f + v2f

Now, we can use the conservation of energy to relate the initial kinetic energy of the system to the final kinetic energy of the system.

The initial kinetic energy K1i and final kinetic energy K1f of ball 1 are given by:

K1i = (1/2) * m * v1i^2
K1f = (1/2) * m * v1f^2

Similarly, the final kinetic energy K2f of ball 2 is:

K2f = (1/2) * m * v2f^2

Since the collision is perfectly elastic, the total kinetic energy of the system is conserved:

K1i + 0 = K1f + K2f

Substituting the expressions for the kinetic energies:

(1/2) * m * v1i^2 = (1/2) * m * v1f^2 + (1/2) * m * v2f^2

Now, let's substitute v1i in terms of v1f + v2f:

(1/2) * m * (v1f + v2f)^2 = (1/2) * m * v1f^2 + (1/2) * m * v2f^2

Expanding and canceling the common terms:

(v1f)^2 + 2 * v1f * v2f + (v2f)^2 = (v1f)^2 + (v2f)^2

Simplifying further:

2 * v1f * v2f = 0

Since the masses and velocities are positive quantities, this equation implies that either v1f = 0 or v2f = 0.

From the given information, we know that the initially moving ball deflects 30° from its original direction. This means that its final velocity has a component in the original direction as well as a component perpendicular to the original direction.

Therefore, we can conclude that v1f ≠ 0. Thus, the only possibility is v2f = 0.

This implies that the initially stationary ball comes to rest after the collision, while the initially moving ball continues to move in a different direction.

Therefore, the speed of the initially stationary ball after the collision is 0 m/s.

1.5

This answer solved by ...mv-mvcos30

2.59