The star of a distant solar system explodes as a supernova .At the moment of the explosion ,an resting exploration spaceship is AU away from the shock wave . The shock wave of the explosion spaceship travels with 25000km/s towards the spaceship .To save the crew , the spacecraft makes use of a special booster that uniformly accelerates at 150m/s^2 in the opposite direction .
Determine if the crew manages to escape from the shock wave (neglect relativistic effects)
Let the x-axis be directed from star to the starship. At the initial moment the coordinate of the ship is and this is the initial distance between the shock and the ship. After the beginning of the acceleration the coordinate of the ship after time t will be
The coordinate of the shock wave is . Let us determine if there is a moment t at which the shock wave reaches the starship:
We calculate the discriminant:
The roots of the equation are
Therefore, after approximately 6000 seconds the shock wave will reach the ship.
Comments