Question

Need correct answer! . Need clear and detailed answer please. I am STILL confused at this. I KNOW that the correct answer is 102.5 mins but how? please explain in simple steps!!

Because parents are concerned that children are learning "wrong" science from TV, you have been asked to be a technical advisor for a science fiction cartoon show on Saturday morning. In the plot, a vicious criminal (Natasha Nogood) escapes from a space station prison. The prison is located between galaxies far away from any stars. Natasha steals a small space ship and blasts off to meet her partners somewhere in deep space. The stolen ship accelerates in a straight line at its maximum possible acceleration of 30 m/sec2. After 10 minutes all of the fuel is burned up and the ship coasts at a constant velocity. Meanwhile, the hero (Captain Starr) learns of the escape while dining in the prison with the warden's daughter (Virginia Lovely). Of course he immediately (as soon as he finishes dessert) rushes off the recapture Natasha. He gives chase in an identical ship, which has an identical maximum acceleration, going in an identical direction. Unfortunately, Natasha has a 30 minute head start. Luckily, Natasha's ship did not start with a full load of fuel. With his full load of fuel, Captain Starr can maintain maximum acceleration for 15 minutes. How long will it take Captain Starr's ship to catch up to Natasha's?

Answer 1

Acceleration, m = 30 m/s²

Initial velocity, u = 0

Distance covered in first 10 minute (600 s) during acceleration = u*t+(1/2)a*t² = 0+ 0.5*30*600² = 5400000m

Speed of spaceship when it stops to accelerate,v = u + at = 0+30*600 = 18000 m/s

Distance covered in further 20 min (1200 s) = vt = 18000 * 1200 = 21600000 m

Distance covered by her before captian starts his journey =  5400000 + 21600000 = 27000000 m

Let total time taken by captain starrs ship to catch natasha be t seconds

Then distance covered by natasha in this additional t s = vt = 18000t

Total distance by natasha = 27000000 + 18000t (EqA)

For the first 15 mins he accelerates

Distance covered by him in 15 min (900 s) = ut+0.5 at² = 0 + 0.5*30*900² = 12150000 m

Speed of captiain starr when he stops accelerating = u+at = 0 +30*900 = 27000 m/s

Distance covered by him in the rest (t-900) s= 27000 * (t-900) = 27000 t - 24300000

So total distance covered by him in t time = 27000 t - 24300000 + 12150000 = 27000 t - 12150000 (EqB)

So from EqA and EqB

27000000 + 18000t = 27000 t - 12150000

=> 9000 t = 39150000

=> t = 4350 seconds = 72.5 minute

Total time = t + head start time = 72.5 + 30 =102.5 minute