Question

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

b. Explain why this is correct.
Please help.

Answer 1

If the astronaut wears a spacesuit, the glasses won't touch the ground.
Do you know gravitational acceleration on Mars? Wikipedia says it's .38 of our gravity at the surface. http://en.wikipedia.org/wiki/Surface_gravity#Mass.2C_radius_and_surface_gravity But do you have another value? Given by the problem or a textbook?

Answer 2

No, I do not have another value. And if the astronaut is not wearing a spacesuit, how long will it take for her glasses to fall to the ground?

Answer 3

Hehe, well, we'll have to use Wikipedia's value then or use another source.

So, what is gravitational acceleration at Earth's surface? What number do you use?

Answer 4

I don't really know.

Answer 5

Do you use

\(\rm{10m/s^2}\)
\(\rm{9.8m/s^2}\)
or
\(\rm{9.81m/s^2}\)
?

Answer 6

10m/s^2?

Answer 7

Okay then.

So, Mars' gravity is 10m/s^2*.38
\(\rm{10m/s^2\times0.38=3.8m/s^2}\)

Do you know how to do this problem if it were on Earth?

Answer 8

No.

Answer 9

Well, \(d=v_it+\frac{1}{2}at^2\).
Does that look familiar?

Answer 10

Not really.

Answer 11

Okay!
\(d\) is the change in the distance of an object. What is that going to be for us?

Answer 12

the glasses? I think.

Answer 13

Yup! And what is their change in distance as they fall?

Answer 14

is it Potential energy?

Answer 15

I'm thinking of a number, actually! I was thinking, how far do the glasses fall?
Also, we need positive and negatives going on... Do you want up to be positive, or down?

Answer 16

Up.

Answer 17

Okay! So, the glasses fall DOWN 2m, so it is a negative 2m change.
\(2=v_it+\frac{1}{2}at^2\)

What is the velocity when they start falling (\(v_i\))?

Answer 18

2m?

Answer 19

Hmm? What is 2m? That is two meters.

Answer 20

Yes?

Answer 21

Haha, that's a question?

Answer 22

No, I am not very sure.

Answer 23

Okay!

And they are not moving to start with, right?

Answer 24

Right.

Answer 25

so that means their velocity is zero. \(v_i=0\).
\(-2=(0)t+\frac{1}{2}at^2\\\implies-2=\frac{1}{2}at^2\)

\(a\) is the gravitational acceleration which is \(-3.8\), we said.

I have to go. I'll be back. Good luck!

Answer 26

Thank you very much.

Answer 27

So now we have
\(-2=\frac{1}{2}(-3.8)t^2\\\implies
-4=-3.8t^2\\\implies
\frac{4}{3.8}=t^2\\\implies t=?
\)
Can you finish solving for \(t\)? And then just use a calculator!