Question

Defiance Drake, Space Adventurer,

desperately needs to reach a cargo vessel 100m away, or run out of air and die in deep space. For our purposes, there are two relevant directions, the direction Defiance is traveling in (the x-direction, at 1 m/s), and direction of the cargo ship's motion, which is perpendicular to her motion (y-direction, 10 m/s). Defiance uses her jet boots, choosing to accelerate directly in the x-direction at 0.25g (she starts at (x=100,y=0)). If the cargo vessel is 25 m long, and its nose cone starts at x=0,y=0, will Defiance reach the ship or miss? If she misses, how should she have chosen her path (assume she cannot exceed 1 g)?