Question

It has been suggested, and not facetiously, that life might have originated on Mars and been carried to Earth when a meteor hit Mars and blasted pieces of rock (perhaps containing primitive life) free of the surface. Astronomers know that many Martian rocks have come to Earth this way. One objection to this idea is that microbes would have 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/s, and this would most likely happen over a distance of about 4.0m during the impact.
1) What would be the acceleration, in m/s, of such a rock fragment?
2) What would be the acceleration, in g's, of such a rock fragment?
3) How long would this acceleration last?
4) In tests, scientists have found that over 40% of Bacillius subtilis bacteria survived after an acceleration of 450000g. In light of your answer to part A, can we rule out the hypothesis that life might have been blasted from Mars to Earth?

Answer 1

Answer and Explanation:

Given that

v_f = 5 km/s = 5,000 m/s

d = 4 m

v_i = 0 m/s

The computation is shown below:

1. The acceleration in m/s is

Here we use the motio third equation which is

$v_f^2 = v_i^2 + 2ad$

5000^2 = 0^2 + 2 (a) (4)

So

$a = 3.125 \times 10^{6} m/s^2$

2. Now acceleration in g is

$= \frac{3.125 \times 10^{6} m/s^2}{9.81}$

$= 3.18 \times 10^{5}g$

3. The long of acceleration last is

$t = \frac{v-u}{a}$

$= \frac{5000 - 0}{3.125 \times 10^{6}}$

$= 1.6 \times 10^{-3}s$

4.As we can see that

$3.18 \times 10^{5}$ is smaller than the $4.5 \times 10^{5}g$

So, it should not be ruled out