Question

A $2\,m$ tall astronaut standing on Mars drops her glasses from her nose. How long will it take the glasses to reach the ground?

Answer 1

In order to answer this question, to calculate the time taken by the glasses to reach the ground, we will first rewrite the given facts related to this question. And then we will apply the formula of the motion.

Formula used:
$S = ut + \dfrac{1}{2}a.{t^2}$
where, $S$ is the distance between the initial position and the ground or height of the astronaut, $u$ is the initial velocity, $a$ is the gravity on mars, as acceleration towards the ground and $t$ is the time for glasses to reach the ground.

Complete step by step answer:
Height of the astronaut, $S = 2\,m$. Acceleration of the glasses to reach the ground is the gravity on Mars, $g = 3.7\,m.{s^{ - 2}}$ , the gravity value for every planet is fixed.And, when the glasses drop, then the initial velocity of the glasses, $u = 0\,m.{s^{ - 1}}$
So, by using the formula of the motion-
$S = ut + \dfrac{1}{2}a.{t^2}$
$\Rightarrow 2 = 0 \times t + \dfrac{1}{2} \times 3.7 \times {t^2} \\\ \Rightarrow 2 = 1.85{t^2} \\\ \Rightarrow t = \dfrac{2}{{1.85}} \\\ \therefore t = 1.0.3\,s \\\$
Hence, the required time for glasses to reach the ground is $1.03\,s$.

Note: Furthermore, the gravity on Mars' surface is far lower than on Earth — 62 percent lower to be precise. A human weighing $100\,kg$ on Earth would weigh just 38 kg on Mars, which is only 0.376 of the Earth standard (or $0.376\,g$ ). The difference in surface gravity is caused by a number of parameters, the most important of which are mass, density, and radius.