Randall D. Knight — Kinematics in One Dimension: Problem Exercise_15

It has been proposed that a very small probe could be sent to a nearby star system by using a powerful laser beam, fired from an earth-orbiting satellite, to push on a lightweight “solar sail.” Very high speeds could be reached in the vacuum of space by a fairly modest acceleration that continues for a long interval of time. a. Write an expression for the constant acceleration \( a_x \) an object needs to reach velocity \( v_{\text{max}} \) in time \( t_{\text{push}} \), starting from rest. b. Write an expression in terms of \( v_{\text{max}} \) and \( t_{\text{push}} \) for the distance \( d \) the object travels during this time. c. For the mission to be feasible, the probe needs to reach 10% of the speed of light after being pushed for 1.0 year. The probe would then coast the rest of the way. What constant acceleration is needed? Note that the speed of light and much other useful data needed to solve problems are given inside the front and back covers of the book. d. What fraction of a light year will the probe have traveled at the end of the year? A light year (ly) is the distance traveled by light in 1 year.