For what value of v does gamma = 1.0295?

Question

For what value of v does gamma = 1.0295? Observe that for speeds lower than this value, time dilation and length contraction are effects amounting to less than 2.95%.

Answer 1

δ = 1 / sqrt ( 1 - v^2 / c^2 )

You know gamma; solve for v (in terms of c)

δ^2 = 1 / ( 1 - v^2 / c^2 )

1 / δ^2 = 1 - v^2 / c^2

v^2 / c^2 = 1 - 1 / δ^2

v^2 = c^2 ( 1 - 1 / δ^2 )

v = c sqrt ( 1 - 1 / δ^2 )