Determine the ratio β = v/c for each of the following. (a) A car traveling 120 km/h.
(b) A commercial jet airliner traveling 270 m/s.
(c) A supersonic airplane traveling mach 2.7. (Mach number = v/vsound. Assume the speed of sound is 343 m/s.)
(d) The space shuttle, traveling 27,000 km/h.
(e) An electron traveling 30 cm in 2 ns.
(f) A proton traveling across a nucleus (10-14 m) in 0.38 ✕ 10-22 s.

a) , b) , c) , d) , e) , f)

Explanation:

From relativist physics we know that is the symbol for the speed of light, which equal to approximately 300000 kilometers per second. (300000000 meters per second).

a) A car traveling 120 kilometers per hour:

At first we convert the car speed into meters per second:

The ratio is now calculated: (, )

b) A commercial jet airliner traveling 270 meters per second:

The ratio is now calculated: (, )

c) A supersonic airplane traveling Mach 2.7:

At first we get the speed of the supersonic airplane from Mach's formula:

Where:

- Mach number, dimensionless.

- Speed of sound in air, measured in meters per second.

If we know that and , then the speed of the supersonic airplane is:

The ratio is now calculated: (, )

d) The space shuttle, travelling 27000 kilometers per hour:

At first we convert the space shuttle speed into meters per second:

The ratio is now calculated: (, )

e) An electron traveling 30 centimeters in 2 nanoseconds:

If we assume that electron travels at constant velocity, then speed is obtained as follows:

Where:

- Speed, measured in meters per second.

- Travelled distance, measured in meters.

- Time, measured in seconds.

If we know that and , then speed of the electron is:

The ratio is now calculated: (, )

f) A proton traveling across a nucleus (10⁻¹⁴ meters) in 0.38 × 10⁻²² seconds:

If we assume that proton travels at constant velocity, then speed is obtained as follows:

Where:

- Speed, measured in meters per second.

- Travelled distance, measured in meters.

- Time, measured in seconds.

If we know that and , then speed of the electron is:

The ratio is now calculated: (, )

thermal energy is the answer