Answer :
Comparing the kinetic energy of a 21,500 kg truck moving at 145 km/h with that of an 82.0 kg astronaut in orbit moving at 27,000 km/h, the ratio observed between the two is 0.0038.
To compare the kinetic energy of the truck and the astronaut, we can use the equation for kinetic energy:
KE = 0.5 * m * [tex]v^2[/tex]
where KE is the kinetic energy, m is the mass, and v is the velocity.
Given:
Mass of the truck ([tex]m_{truck[/tex]) = 21,500 kg
Velocity of the truck ([tex]v_{truck[/tex]) = 145 km/h = 145,000 m/h
Mass of the astronaut ([tex]m_{astronaut[/tex]) = 82.0 kg
Velocity of the astronaut ([tex]v_{astronaut[/tex]) = 27,000 km/h = 27,000,000 m/h
Calculating the kinetic energy for the truck:
[tex]KE_{truck}[/tex] = 0.5 * [tex]m_{truck[/tex]* [tex]v_{truck^2\\[/tex]
[tex]KE_{truck}[/tex] = [tex]0.5 * 21,500 kg * (145,000 m/h)^2[/tex]
Calculating the kinetic energy for the astronaut:
[tex]KE_{astronaut}[/tex] = 0.5 * [tex]m_{astronaut[/tex] * [tex]v_{astronaut[/tex]²
[tex]KE_{astronaut}[/tex]= [tex]0.5 * 82.0 kg * (27,000,000 m/h)^2[/tex]
Now we can calculate the ratio of the kinetic energies:
[tex]KE_{astronaut} / KE_{truck}[/tex] =[tex](0.5 * 82.0 kg * (27,000,000 m/h)^2) / (0.5 * 21,500 kg * (145,000 m/h)^2)[/tex]
Simplifying the equation:
[tex]KE_{astronaut} / KE_{truck}[/tex] ≈ [tex](82.0 kg * (27,000,000 m/h)^2) / (21,500 kg * (145,000 m/h)^2)[/tex]
[tex]KE_{astronaut} / KE_{truck}[/tex] ≈[tex](82.0 / 21,500) * ((27,000,000 / 145,000)^2)[/tex]
Calculating the ratio:
[tex]KE_{astronaut} / KE_{truck}[/tex] ≈ 0.0038
Therefore, the ratio of the kinetic energy of the astronaut to the kinetic energy of the truck is approximately 0.0038.
Learn more about kinetic energy here:
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