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 s he finishes dessert) rushes off the recapture Natasha. He chose 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?
For Natasha's space ship constant velocity (v1), by using
v = u +a*t
v = v1 = ?,
u = 0,
t = 10 min = 10*60 = 600 sec,
a = 30m/s^2
=> v1 = 0 + 30*600 = 18000 m/s == 18 km/s
In first 10 min, distance travelled by Natasha,
s = ut + 1/2 a t^2
s = s11 = 0*600 + (1/2)*30*(600)^2 = 5400000 m == 5400 km
in 20 min (=30-10) distance travelled by Natash,
s12 = v1*20*60 = 18000*20*60 = 21600000 m == ...
A hypothetical, physics fiction problem is solved.