Finding the Velocity of an Asteroid with a Given Mass and Kinetic Energy

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To find the velocity of an asteroid with a mass of 2500 kg and a relativistic kinetic energy of 1e+20 J, the equation KE=(mc^2/sqrt(1-v^2/c^2)-mc^2 is used. The calculated result of 216480727.3 m/s appears excessively high, as velocities are typically expressed as a fraction of the speed of light (c). Concerns arise regarding potential errors in unit conversion or algebraic manipulation. Clarification is sought on the mathematical steps taken to reach this result, indicating that the issue may lie in the algebra involved. Accurate calculations are crucial for determining the correct velocity in terms of c.
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Homework Statement



An asteroid of mass 2500 kg has a (relativistic) kinetic energy of 1e+20 J. What is the speed of the asteroid?

Homework Equations



KE=(mc^2/sqrt(1-v^2/c^2)-mc^2

The Attempt at a Solution



I tried plugging in my values to this equation and got 216480727.3. the answer is in terms of c. I am not sure if I am doing something wrong or if I am in the wrong units because in all my problems where I am given a velocity its always a small value times c such as .9c and I got a large number. There is another problem like this where I am solving for the velocity I can't figure out either.
 
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sklotz said:

Homework Statement



An asteroid of mass 2500 kg has a (relativistic) kinetic energy of 1e+20 J. What is the speed of the asteroid?

Homework Equations



KE=(mc^2/sqrt(1-v^2/c^2)-mc^2

The Attempt at a Solution



I tried plugging in my values to this equation and got 216480727.3. the answer is in terms of c. I am not sure if I am doing something wrong or if I am in the wrong units because in all my problems where I am given a velocity its always a small value times c such as .9c and I got a large number. There is another problem like this where I am solving for the velocity I can't figure out either.

Show us the mathematical steps you used to arrive at this result. This seems to be an algebra issue.
 

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