Universal Gravitation Problem (Grade 11)

[danielle_54321]

Homework Statement

If you threw something vertically upward from the moon's surface where g=1.6N/kg [down], how many times higher would it reach compared to throwing it from the surface of the Earth with the same force? Neglect the effect of air resistance on the Earth.

Homework Equations

I don't know which equations to use. Without other variables, I don't know where to start. I am not necessarily looking for a solution, I just need help at getting my solution started.
I do know that
g=9.81N/kg on earth.
F=ma is likely a relevant equation, becuase g is an acceleration and the force and mass are both constants.

The Attempt at a Solution

g(earth)/ gmoon
=9.81/1.6
=6.13125

Does this make sense? The solution seems much too simple. :(

 

[denverdoc]

well, sometimes one gets lucky. for more rigor, you might add kinematics expression relating distance and velocity, such as v^2=2*a*h where v is the initial velocity the rock or whatever was thrown upwards.

 

[danielle_54321]

Okay, thank-you.

So, if I do not have any other varables (height, acceleration, force, time, distance, initial velocity or final velocity) is my answer the most accurate possible?

Also, do you think I should factor in:

Fg = (G*m1*m2)/d^2

where G is the gravitational constant (6.67 x 10^-11) and m1 is the mass of the planet and m2 is the mass of the object thrown and d is the distance between the mass' centre and the centre of the object?


In order to do any further calculations, would it profit me to determine the mass and radius of both the moon and the earth?

I don't know if that makes any sense or not?

 

[vivesdn]

g already is G*m1/d^2. An it is fair to assume that the initial impulse is not powerful enogh to reach an altitude for which you need to consider any variation on d.

If you want, you can calculate the highest point for both situations. You will get that result again. Or using the formula by denverdoc, as you have the same initial speed, it is easy to see that 'a' and 'h' wil be inversely related.