Answer to Question #165249 in Astronomy | Astrophysics for mahmoud

Question #165249

The star of a distant solar system explodes as a supernova. At the moment of the explosion, an resting exploration spaceship is 15 AU away from the shock wave. The shock wave of the explosion travels with 25000 km/s towards the spaceship. To save the crew, the spacecra makes use of a special booster that uniformly accelerates at 150 m/s2 in the opposite direction. Determine if the crew manages to escape from the shock wave. (Neglect relativistic eects.) 


1
Expert's answer
2021-02-22T10:23:17-0500

Let's consider the situation from the frame of reference of the wave. In this frame it does not move and the ship approaches it with the speed of "v = -25000km\/s = -2.5\\times 10^7m\/s". In order to be in safety, it should achieve a zero speed in this frame. This will happen in time:



"t = \\dfrac{0-v}{a} = \\dfrac{-v}{a}"

where "a = 150m\/s^2" is the acceleration of the ship. In this time the ship covers the following distance (toward the wave):



"d = vt + \\dfrac{at^2}{2} = -\\dfrac{v^2}{a}+\\dfrac{v^2}{2a} = -\\dfrac{v^2}{2a}\\\\\nd = -\\dfrac{(2.5\\times 10^7)^2}{150}\\approx 4.2\\times 10^{12}m"

Since 15 AU is approximately "2.2\\times 10^{12}m" the crew does not manage to escape from the shock wave.


Answer. does not manage.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS