Question

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).

Answer 1

(a). An automobile speed as a function of speed of light is
`8.61*10^(-8)\ m/s`

(b). The speed of sound as a function of speed of light is
`10.9*10^(-8)\ m/s`

(c). The escape velocity of a rocket as a function of speed of light is
`4.03*10^(-8)\ m/s`

(d). The orbital speed of the Earth about the Sun is
`3*10^(8)\ m/s`

Step-by-step 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

`c=3*10^(8)\ m/s`

(a). Automobile speed = 93 km/h

Speed
`v_(a)=93*(5)/(18)`

`v_(a)=25.83\ m/s`

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

Using formula of speed

`v=(v_(a))/(v_(l))`

Put the value into the formula

`v=(25.83)/(3*10^(8))`

`v=8.61*10^(-8)\ m/s`

(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

`v=(v_(s))/(v_(l))`

Put the value into the formula

`v=(329)/(3*10^(8))`

`v=10.9*10^(-8)\ m/s`

(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

`v=(v_(e))/(v_(l))`

Put the value into the formula

`v=(12.1)/(3*10^(8))`

`v=4.03*10^(-8)\ m/s`

(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

`v=(d)/(t)`

Put the value into the formula

`v=(1.5*10^(8)*1000)/(500)`

`v=3*10^(8)\ m/s`

Hence, (a). An automobile speed as a function of speed of light is
`8.61*10^(-8)\ m/s`

(b). The speed of sound as a function of speed of light is
`10.9*10^(-8)\ m/s`

(c). The escape velocity of a rocket as a function of speed of light is
`4.03*10^(-8)\ m/s`

(d). The orbital speed of the Earth about the Sun is
`3*10^(8)\ m/s`