Express the following speeds as a function of the speed of light, c: (a) an automobile speed (93 km/h) (b) the speed of sound (329 m/s) (c) the escape velocity of a rocket from the Earth's surface (12.1 km/s) (d) the orbital speed of the Earth about the Sun (Sun-Earth distance 1.5×108 km).

(a). An automobile speed as a function of speed of light is

(b). The speed of sound as a function of speed of light is

(c). The escape velocity of a rocket as a function of speed of light is

(d). The orbital speed of the Earth about the Sun is

Explanation:

Given that,

Express the following speeds as a function of the speed of light.

Automobile speed = 93 km/h

We know that,

A function of speed of light is

(a). Automobile speed = 93 km/h

Speed

We need to express the speed of automobile speed as a function of speed of light

Using formula of speed

Put the value into the formula

(b). The speed of sound is 329 m/s.

We need to express the speed of sound as a function of speed of light

Using formula of speed

Put the value into the formula

(c). The escape velocity of a rocket from the Earth's surface is 12.1 m/s

We need to express the speed of sound as a function of speed of light

Using formula of speed

Put the value into the formula

(d). The orbital speed of the Earth about the Sun

Distance = 1.5\times10^{8}[/tex]

We know that,

The sun rays reached on the earth in 8 min 20 sec.

We need to express the speed of sound as a function of speed of light

Using formula of speed

Put the value into the formula

Hence, (a). An automobile speed as a function of speed of light is

(b). The speed of sound as a function of speed of light is

(c). The escape velocity of a rocket as a function of speed of light is

(d). The orbital speed of the Earth about the Sun is