Question #163133

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 spacecraft 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 effects.)


1
Expert's answer
2021-03-12T09:32:55-0500

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=2.5×107m/sv = -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=0va=vat = \dfrac{0-v}{a} = \dfrac{-v}{a}

where a=150m/s2a = 150m/s^2 is the acceleration of the ship. In this time the ship covers the following distance (toward the wave):


d=vt+at22=v2a+v22a=v22ad=(2.5×107)22×1502.1×1012md = vt + \dfrac{at^2}{2} = -\dfrac{v^2}{a}+\dfrac{v^2}{2a} = -\dfrac{v^2}{2a}\\ d = -\dfrac{(2.5\times 10^7)^2}{2\times150}\approx 2.1\times 10^{12}m

Since 15 AU is approximately 2.2×1012m2.2\times 10^{12}m the crew does not manage to escape from the shock wave.


Answer. does not manage.


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Comments

Synyster
11.03.21, 18:00

Wrong, There will be "2a" but you calculated as only "1a" in the last line.

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