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/s, and that would most likely happen over a distance of about 3.0 m during the meteor impact.

A) What would be the acceleration, in m/s, of such a rock fragment?
B) What would be the acceleration, in g's, of such a rock fragment?

Answer 1

(a) a = 4.16 x 10⁶ m/s²

(b) a = 4.25 x 10⁵ g

Step-by-step explanation:

(a)

We use third equation of motion to find the acceleration of rock fragments:

2as = Vf² - Vi²

where,

a = acceleration = ?

s = distance covered = 3 m

Vi = Initial Speed = 0 m/s

Vf = Final Speed = 5 km/s = 5000 m/s

Therefore,

2a(3 m) = (5000 m/s)² - (0 m/s)²

a = (2.5 x 10⁷ m²/s²)/6 m

a = 4.16 x 10⁶ m/s²

(b)

converting this value in terms of g:

a = (4.16 x 10⁶ m/s²)(g/9.8 m/s²)

a = 4.25 x 10⁵ g