Because parents are concerned that children are learning \'\'wrong\" science fro

Question

Because parents are concerned that children are learning ''wrong" science from TV, you have been asked to be a technical advisor for a new science fiction show. The show takes place on a space station at rest in deep space far away from any stars. In the plot, a vicious criminal escapes from the space station prison. She steals a small space ship and blasts off to meet her partners somewhere in deep space. Your job is to calculate how long her partners have to transport her off her ship before it is destroyed by a photon torpedo from the space station? In the story, the stolen ship accelerates in a straight line at its maximum possible acceleration of 30m/sec2 After 10 minutes all of the fuel is burned and the ship coasts at a constant velocity. Meanwhile, the hero learns of the escape and fires a photon torpedo. Once fired, a photon torpedo travels at a constant velocity of 20,000 m/s. By that time the escapee has a 30 minute head start on the photon torpedo.

Explanation / Answer

Velocity of the escapee after 10 minutes,

v = u + at = 0 + 30(10 x 60) = 18000 m/s

so total distance covered by the escapee in 30 minutes will be: D = [ut + (1/2)at2] + vt

=> D = 0 + (1/2)(30)(10 x 60)2 + 18000(20 x 60) = 27 x 106 m

also, let t be the time after the photon torpedo is fired when the spaceship of the escapee is destroyed.

then, 27 x 106 + 18000t = 20000t

=> t = 13500s = 225 minutes.

so her partners have to transport her for 225+30 = 255 minutes until it is destroyed by the photon torpedo.

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