Question

Problem 28.3 Suppose that you are planning a trip in which a spacecraZ is to travel at a constant velocity for exactly six months, as measured by a clock on board the spacecraZ, and then return home at the same speed. Upon your return, the people on earth will have advanced exactly one hundred years into the future. According to special relaEvity, how fast must you travel? Express your answer to five significant figures as a mulEple of c – for example, 0.95585c.

Answer 1

Answer:

v = 0.999981c m/s

Explanation:

Using the time dilation equation

$T = \frac{T_{0} }{\sqrt{1 - \frac{v^{2} }{c^{2} } } }$

T = stationary time = 100 years

T₀ = 11/12 years = 0.917 years

v = speed of travel in the space = ?

c = speed of light = 3 * 10⁸ m/s

$100 = \frac{0.917 }{\sqrt{1 - \frac{v^{2} }{(3*10^{8} )^{2} } } }$

$(0.917/100) ^{2} = 1 - \frac{v^{2} }{ 9 * 10^{16} }$

v = 299987395.57 m/s

v = 2.99 * 10⁸ m/s

v = 0.999981c m/s