Question

It has been suggested, and not facetiously, that life might have originated on Mars and been carried to the earth when a meteor hit Mars and blasted pieces of rock (perhaps containing primitive life) free of the Martian surface. Astronomers know that many Martian rocks have come to the earth this way. (For instance, search the Internet for "ALH 84001.") One objection to this idea is that microbes would have had to undergo an enormous lethal acceleration during the impact. Let us investigate how large such an acceleration might be. To escape Mars, rock fragments would have to reach its escape velocity of 5.0 km/skm/s, and that would most likely happen over a distance of about 3.0 mm during the meteor impact.

a) What would be the acceleration (in m/s2m/s2) of such a rock fragment, if the acceleration is constant?

b) What would be the acceleration in gg's?

c) How long would this acceleration last?

Answer 1

Initial velocity before the impact, u = 5 km/s = 5000 m/s
Final velocity after the impact, v = 0
Distance travelled, s = 3 m

a)
Using the formula, v² - u² = 2 * a * s,
0 - 5000² = 2 * a * 3
a = - 4.17 * 10⁶ m/s²
|a| = 4.17 * 10⁶ m/s²

b)
a_g * g = a
Where a_g is the acceleration in g's , g is acceleration due to gravity.
a_g = a/g
= (4.17 * 10⁶) / 9.81
= 4.25 * 10⁵

a = 4.25 * 10⁵ g

c)
Consider t as the time.
t = (v - u) / a
= (0 - 5000) / (- 4.17 * 10⁶)
= 1.2 * 10^-3 s