Question

A 2-meter-tall astronaut standing on Mars drops her glasses from her nose. How long will it take the glasses to reach the ground?

Answer 1

1 sec

Explanation:

She must not be without her suit in open Mars air. Jokes apart, Provided her reflex is not good enough, it takes about 1 sec .

Lets calculate how much time it will take in earth.

time of descent = `t = sqrt(2h/g) = sqrt(4/9.8)sec.~~0.65 sec`

Now for Mars, lets calculate the g

We know `g = (GM)/R^2` so

`(g_m/g_e )= (M_m/M_e)/(R_m/R_e)^2 ~~ 0.1/0.5^2=0.4`

(Which, of course I did not remember, ref: http://nssdc.gsfc.nasa.gov/planetary/factsheet/planet_table_ratio.html)

And now from the formula for time of descent, we know

`t_m/t_e = sqrt(1/(g_m/g_e)) = sqrt(1/0.4) ~~1.58`

So `t_m = t_e*1.58 = 0.65*1.58 sec ~~ 1.02 sec`