Question

If an object's kinetic energy is 88% of rest energy, how fast is It going?

Answer 1

relativistic kE

kE = m c^2 ( 1/ sqrt ( 1 - v^2/c^2) - 1)

0.88 m c^2 = m c^2 ( 1 / sqrt ( 1 - v^2/c^2) - 1)

0.88 = 1 / sqrt ( 1 - v^2/c^2) - 1

0.88 + 1 = 1 / sqrt (1 - v^2/c^2)

sqrt ( 1 - v^2/c^2) = 1 / 1.88

sqrt ( 1 - v^2/c^2) = 0.53191

on squaring both side

1 - v^2/ c^2 =0.53191^2

1 - v^2 / c^2 = 0.282933

1 - 0.282933 = v^2/c^2

v^2 / c^2 = 0.7170665

taking sqrt both side

v/c = sqrt ( 0.7170665) = 0.8468

v = 0.8468 c

v = 2.54* 10^8 m/s

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