Suppose you are planning a trip in which a spacecraft is to travel at a constant velocity for exactly six months, as measured by a clock on board the spacecraft, and then return home at the same speed. Upon return, the people on earth will have advanced exactly 110 years into the future. According to special relativity, how fast must you travel

0.999958c

Explanation:

Remember that the trip involves traveling for six months at a constant velocity thus returning home at same speed. The time interval of this trip will therefore be one year.

Accurate time interval to be measured by the clock on the spaceship Δt0 = 1.0 years

Time interval as advanced on earth observed from the spacecraft Δt = 110 years

the formula for time dilation is

Δt = Δt0 / √ (1-v2/c2)

or v = c*√1 - (Δt0/Δt) 2

=c*√[1 - (1year/110years) 2]

= 0.999958c