A cue ball (mass = 0.140 kg) is at rest on a frictionless pool table. The ball is hit dead center by a pool stick which applies an impulse of +1.60 N·s to the ball. The ball then slides along the table and makes an elastic head-on collision with a second ball of equal mass that is initially at rest. Find the velocity of the second ball just after it is struck.

To find the velocity of the second ball just after it is struck, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is given by the product of its mass and velocity. Let's assume the initial velocity of the cue ball is 0 m/s, and the initial velocity of the second ball is also 0 m/s. We need to find the final velocity of the second ball.

Step 1: Determine the momentum of the cue ball just before the collision.
The impulse applied to the cue ball is equal to the change in momentum. We can use the impulse-momentum equation: Impulse = Change in momentum.
Impulse = 1.60 N·s
Change in momentum = mass × change in velocity

Since the initial velocity is 0 m/s, the change in velocity is the final velocity.
Change in momentum = 0.14 kg × final velocity

Setting impulse equal to change in momentum, we get:
1.60 N·s = 0.14 kg × final velocity

Step 2: Calculate the final velocity of the cue ball.
Solving for final velocity:
final velocity = 1.60 N·s / 0.14 kg
final velocity ≈ 11.43 m/s

Step 3: Apply the conservation of momentum to find the final velocity of the second ball.
Since the second ball is initially at rest, the total momentum before the collision is only the momentum of the cue ball:
Initial momentum = mass × velocity = 0.14 kg × 11.43 m/s

According to the principle of conservation of momentum, the total momentum after the collision is also equal to 0.14 kg × final velocity of the second ball.

Setting the two momenta equal to each other, we can solve for the final velocity of the second ball:
0.14 kg × 11.43 m/s = 0.14 kg × final velocity of the second ball

Simplifying the equation:
11.43 m/s = final velocity of the second ball

Therefore, the velocity of the second ball just after it is struck is approximately 11.43 m/s.