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. (For information on one of these, search the Internet for “ALH 84001”.) 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 4.0 m during the impact.
average speed during deceleration = 2.5*10^3 m/s
time is then 4 m/2.5*10^3 m/s = 1.6*10^-3 seconds to stop
a = - 5*10^3/1.6*10^-3 = -3.125*10^6 m/s^2
= - 3,125,000 m/s^2:)
To investigate the acceleration required for rock fragments to reach the escape velocity of Mars, we can use the basic equations of motion. The formula we will use is:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity
a = acceleration
s = distance traveled
In this case, the initial velocity (u) is considered to be zero since the rock fragments start from rest. The final velocity (v) is the escape velocity of Mars, which is 5.0 km/s. The distance traveled (s) during the impact is 4.0 m.
Now, let's rearrange the equation to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (5.0 km/s)^2 / (2 * 4.0 m)
To proceed with the calculation, we need to convert the units to be consistent. Let's convert 5.0 km/s to m/s:
5.0 km/s = 5.0 * 1000 m/s = 5000 m/s
Now, we can substitute this value and calculate the acceleration (a):
a = (5000 m/s)^2 / (2 * 4.0 m)
a = 1.25 × 10^7 m^2/s^2 / 8.0 m
a = 1.5625 × 10^6 m/s^2
Therefore, the acceleration required for the rock fragments to reach the escape velocity of Mars over a distance of 4.0 m during impact is approximately 1.5625 × 10^6 m/s^2.
To calculate the acceleration required for rock fragments to reach Mars' escape velocity over a distance of 4.0 m during impact, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (5.0 km/s or 5000 m/s)
u = initial velocity (assumed to be zero)
a = acceleration
s = distance (4.0 m)
Rearranging the equation to solve for acceleration (a), we have:
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (5000^2 - 0) / (2 * 4.0)
Simplifying:
a = (25,000,000 - 0) / 8.0
a = 3,125,000 m/s^2
Therefore, the required acceleration for rock fragments to reach Mars' escape velocity over a distance of 4.0 m during impact would be approximately 3,125,000 m/s^2.