Equation Rearrangement problem(I think)

[ZenMode]

Homework Statement

The escape velocity for tomahawk missile is which escape the gravitational attraction of the Earth is expressed by

v=kg^xr^y
r= radius of Earth , g = acceleration due to gravity k,x,y=dimensionless constants
Determine values for x and y

Homework Equations

I know velocity is displacement/time , and acceleration is velocity/time, however I have no idea how this relates to the question. Since there are no exact values given, I'm pretty sure I have to isolate x and y.

The Attempt at a Solution

v=kg^xr^y

kg^xr^y/kr^y = v/kr^y

g^x=v/kr^y
[/B]
This is where I got stuck.Based on the equation above, then kr^y is the value for Time. I have no idea how I'm supposed to isolate the x and y. And I'm not even sure I'm approaching this question correctly

 

[kuruman]

Use dimensional analysis. What are the dimensions of acceleration multiplied by distance?

 

[TSny]

You need to find values of x and y so that the left-hand side and the right-hand side of v = kg^xr^y have the same dimensions.

For example, suppose you were to let x = 1 and y = 1. What would be the dimensions of the right-hand side?

 

[ZenMode]

You need to find values of x and y so that the left-hand side and the right-hand side of v = kg^xr^y have the same dimensions.

For example, suppose you were to let x = 1 and y = 1. What would be the dimensions of the right-hand side?

Wouldn't that break the rules of the question?
The question never did say x and y are equal.

 

[patric44]

r= radius of Earth , g = acceleration due to gravity k,x,y=dimensionless constants

are you sure that g in that equation is g the acceleration . not G the gravitational constant
i think its G
becouse the escape velocity _Ve=(2GM/r)^0.5
and you can rearange that to get :

i guess its not that simple

 

[TSny]

The question never did say x and y are equal.

True. But it never said they couldn't be equal either.
Anyway, in solving the problem you will determine whether or not they happen to be equal.

 

[TSny]

Hello, patric44. It appears from the statement of the problem that g represents the acceleration due to gravity (apparently at the surface of the earth).

When helping someone with a question, please don't provide a complete solution. This is against the rules of the forum. Try to provide just enough assistance to get the questioner on track. Thanks.

 

[patric44]

Hello, patric44. It appears from the statement of the problem that g represents the acceleration due to gravity (apparently at the surface of the earth).

When helping someone with a question, please don't provide a complete solution. This is against the rules of the forum. Try to provide just enough assistance to get the questioner on track. Thanks.

i don't think that a truly complete solution i mean its only one equation.
i only wanted to show him if it was G it will be much simpler ... sorry any way :)

 

[Mark44]

When helping someone with a question, please don't provide a complete solution. This is against the rules of the forum. Try to provide just enough assistance to get the questioner on track. Thanks.

Noted.