Question

What is the velocity of a 0.400-kg billiard ball if its wavelength is 7.50 cm (large enough for it to interfere with other billiard balls)?

a) 2.34 m/s
b) 3.76 m/s
c) 5.12 m/s
d) 6.98 m/s

Answer 1

The velocity of a billiard ball can be determined using the equation: velocity = wavelength × frequency. The given wavelength of 7.50 cm must be converted to meters. The velocity of the billiard ball is 3.00 × 108 m/s.

Step-by-step explanation:

The velocity of a billiard ball can be determined using the equation:

velocity = wavelength × frequency

To use this equation, it is important to note that the given wavelength of 7.50 cm must be converted to meters. Since 1 meter is equal to 100 centimeters, the wavelength is 0.075 meters. The frequency of a billiard ball is not provided, but it can be calculated using the speed of light, which is approximately 3.00 × 108 meters per second.

To calculate the frequency, divide the speed of light by the wavelength:

frequency = (3.00 × 108 m/s) / (0.075 m)

Simplifying this equation gives:

frequency = 4.00 × 109 Hz

Now, substitute the values for wavelength and frequency into the velocity equation:

velocity = (0.075 m) × (4.00 × 109 Hz)

velocity = 3.00 × 108 m/s

Therefore, the velocity of the billiard ball is 3.00 × 108 m/s.