Question

Zeta Anderson, futuristic super-spy for the Terran Confederation needs to reach her stealth vessel 100m away, or risk either discovery, or running out of air in deep space. For our purposes, there are two relevant directions, the direction Zeta is traveling in (the x-direction, at 1 m/s), and direction of the stealth ship's motion, which is perpendicular to her motion (y-direction, 10 m/s). This is strange as she left orders for the ship to remain stationary with respect to the Zorn ship. Zeta uses her jet-pack, choosing to accelerate directly in the x-direction at 0.25g (she starts at (x=100,y=0)). If the stealth vessel is 25 m long, and its nose cone starts at x=0,y=0, will Zeta reach the ship or miss? If she misses, how should she have chosen her path (assume she cannot exceed 1 g)?

Answer 1

Zeta's initial velocity, u = 1m/s
Acceleration, a = 0.25 g = 2.4525 m/s².
Distance she need to travel, s = 100 m
Consider the final velocity when she reaches x = 0, y = 0 as v
v² - u² = 2as
v = SQRT[2 x 2.4525 x 100 + 1]
= 22.17 m/s
Time taken by Zeta to reach at x = 0 and y = 0 is,
t = (v - u)/a
= (22.17 - 1) / 2.4525
= 8.63 s

Time taken by stealth ship when its tail comes at x = 0 and y = 0 is,
t = 25/10 = 2.5 s

So, she will miss the ship since she will take longer to reach there.
If she makes an angle with respect to her direction, she will reach the ship