Question

Several volcanoes have been observed erupting on the surface of a planet's closest moon. Suppose that material ejected from one of these volcanoes reaches a height of 4.20 km after being projected straight upward with an initial speed of 205 m/s. If the radius of this moon is 4211 km, outline a strategy that allows you to calculate the mass of Io.

Answer 1

How can I calculate the mass of the planet, if I don't have a mass of a second body..

Answer 2

use distance formulas .. to calculate acceleration ... use acceleration due to gravity to calculate mass of moon

Answer 3

I'm having trouble finding which distance formula to use.

Answer 4

v^2 = u^2+2as
V = 0, s = 4200

Answer 5

Is it d = vt + (1/2)at^2?

Answer 6

don't bother with time

Answer 7

In your equation, what is u, and what is s? And how did you get 4200?

Answer 8

u is given ... initial velocitu ... s is distance in meters ... change km in m

Answer 9

or sorry, u is 205m/s?

Answer 10

Wait a second. Using Newton's Universal Law of Gravitation, what is the expression for the acceleration due to gravity, an expression that involves the moon's mass?

Answer 11

All I know is g=9.8, but I don't think that applies here..

Answer 12

It most emphatically does not. You will need Newton's ULG.

Answer 13

no ... that does not apply here

Answer 14

it has a new value ... find it using above formula

Answer 15

So you mean F=Gm1m2/r^2?
I don't know how to use that here, because I don't have a second mass.

Answer 16

and u is 205

Answer 17

but how do I find v?

Answer 18

change F = m1 a ... and cancel out m1 ... you will have m2 ,,, which is to be found out.

Answer 19

hmm