1. The Starship USS Enterprise is travelling in a straight flight path through the Delta Quadrant to investigate the Sontaran Nebula when its sensors detect a disturbance in the fabric of the space-time continuum. Captain Jean Luc Picard orders Lt. Commander Data to reverse course. However, as Data does this, the effect of the disturbance overtakes Enterprise.
Instantaneously, the crew and ship find themselves flying towards the point at which they detected this disturbance but from the opposite direction. Once again Captain Picard orders Data to reverse course and explain what has happened.
Data says, "Captain, my positronic circuits show that we have experienced a displacement phenomenon modelled by the mathematical function
s is our displacement in 1000s of km from the moment we detected the disturbance and t is the time elapsed in minutes. We are now back on course but displaced in parallel by 2000km."
(a) As Data reverses course the first time, Enterprise continues its forward motion for some minutes then returns the way it came. After how many minutes, correct to three significant figures, does Enterprise return to the point at which its sensors first detected the disturbance?
(b) After how many minutes does the effect of the disturbance overtake Enterprise?
(c) Data reverses course twice. Exactly when does Enterprise actually turn? Give your answers correct to three decimal places.
(d) What is the expression for the final course on which Enterprise is travelling?
(e) Data said, "We are back on course but displaced in parallel by 2000km". What was the original course and why does he say it is displaced by 2000?
(f) Captain Picard asks Data to display their displacement time graph on a monitor. Sketch and annotate what he would see for
0 ≤ t ≤ 10 and 0 ≤ s ≤ 34.
Displacement as a function of time is clearly assessed. What the enterprise actually turns is determined.