Final answer:
At one half the speed of light, it would take 8 years to reach a star that is 4 light-years away, because a light-year is the distance light travels in one year, and at half the speed, the journey would take twice as long. So, the correct option is c).
Step-by-step explanation:
If you travel at one-half the speed of light, the time it takes to reach a star which is 4 light-years away can be calculated using the concept of light travel time. A light-year is the distance that light travels in one year, which is about 9.5 trillion kilometers. Given that light travels this distance in one year, at half the speed of light, this journey would take twice the amount of time.
Therefore, for a star that is 4 light-years away, it would take light from that star 4 years to reach us. If you are traveling at half the speed of light, you will be covering that distance at a slower rate, specifically half the rate of light. This means it will take you 2 years to cover 1 light-year. Consequently, to cover 4 light-years, it will take you 4 times longer than it would take light to cover 1 light-year, which is 8 years in total. So, the correct option for this question is C. 8 years, as traveling at one half the speed of light would take this amount of time to reach the star that is 4 light-years away.