Respuesta :
Answer:
(a). An automobile speed as a function of speed of light is [tex]8.61\times10^{-8}\ m/s[/tex]
(b). The speed of sound as a function of speed of light is [tex]10.9\times10^{-8}\ m/s[/tex]
(c). The escape velocity of a rocket as a function of speed of light is [tex]4.03\times10^{-8}\ m/s[/tex]
(d). The orbital speed of the Earth about the Sun is [tex]3\times10^{8}\ m/s[/tex]
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
[tex]c=3\times10^{8}\ m/s[/tex]
(a). Automobile speed = 93 km/h
Speed [tex]v_{a}=93\times\dfrac{5}{18}[/tex]
[tex]v_{a}=25.83\ m/s[/tex]
We need to express the speed of automobile speed as a function of speed of light
Using formula of speed
[tex]v=\dfrac{v_{a}}{v_{l}}[/tex]
Put the value into the formula
[tex]v=\dfrac{25.83}{3\times10^{8}}[/tex]
[tex]v=8.61\times10^{-8}\ m/s[/tex]
(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
[tex]v=\dfrac{v_{s}}{v_{l}}[/tex]
Put the value into the formula
[tex]v=\dfrac{329}{3\times10^{8}}[/tex]
[tex]v=10.9\times10^{-8}\ m/s[/tex]
(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
[tex]v=\dfrac{v_{e}}{v_{l}}[/tex]
Put the value into the formula
[tex]v=\dfrac{12.1}{3\times10^{8}}[/tex]
[tex]v=4.03\times10^{-8}\ m/s[/tex]
(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
[tex]v=\dfrac{d}{t}[/tex]
Put the value into the formula
[tex]v=\dfrac{1.5\times10^{8}\times1000}{500}[/tex]
[tex]v=3\times10^{8}\ m/s[/tex]
Hence, (a). An automobile speed as a function of speed of light is [tex]8.61\times10^{-8}\ m/s[/tex]
(b). The speed of sound as a function of speed of light is [tex]10.9\times10^{-8}\ m/s[/tex]
(c). The escape velocity of a rocket as a function of speed of light is [tex]4.03\times10^{-8}\ m/s[/tex]
(d). The orbital speed of the Earth about the Sun is [tex]3\times10^{8}\ m/s[/tex]
