Question

In a game of pool, a 0.4 kg cue ball is traveling at 0.80 m/s when it hits a slower striped ball moving at 0.38 m/s. after the collision, the striped ball moves off at 0.62 m/s. what is the magnitude of the final velocity of the cue ball? assume all pool balls have the same mass. 0.20 m/s 0.56 m/s 1.0 m/s 1.8 m/s

1. The magnitude of the final velocity of the cue ball is (B) 0.56m/s.

### What is Velocity

• The definition of velocity is a vector measurement of the rate and direction of motion.
• It is a moving body’s speed and direction of motion.
How to calculate the magnitude of the final velocity?
The magnitude of the final velocity can be calculated by following the steps:
• The mass of the cue ball given is 0.4kg.
• The velocity of the cue ball given is +0.80m/s.
• The velocity of the striped ball before the collision is +0.38 m/s.
• The velocity of the striped ball after collision is +0.62m/s.
• We need to find the magnitude of the final velocity of the cue ball.
Assuming all pool balls have the same mass: 0.4kg
Let the final velocity of the cue ball be x.
Now, To find the final velocity:
• Mass of the cue ball × initial velocity of cue ball + Mass of striped ball + initial velocity of striped ball = mass of cue ball × final velocity + mass of striped ball × final velocity of the striped ball
• (0.40)×(0.80)+(0.4)(0.38) = (0.4)(x)+(0.4)(0.62)
• 0.32+0.152=0.4x+0.248
• 0.472=0.4x+0.248
• 0.472-0.248= 0.4x
• 0.224/0.4 =x
• x = 0.56m/s
Therefore, the magnitude of the final velocity of the cue ball is (B) 0.56m/s.
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The correct question is given below:
In a game of pool, a 0.4 kg cue ball is traveling at +0.80 m/s when it hits a slower striped ball moving at +0.38 m/s. After the collision, the striped ball moves off at +0.62 m/s. What is the magnitude of the final velocity of the cue ball? Assume all pool balls have the same mass.
A. 0.20 m/s
B. 0.56 m/s
C. 1.0 m/s
D. 1.8 m/s