# Equation Rearrangement problem(I think)

1. May 14, 2017

### ZenMode

1. The problem statement, all variables and given/known data
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
2. Relevant 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.

3. The attempt at a solution

v=kg^xr^y

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

g^x=v/kr^y

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

2. May 14, 2017

### kuruman

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

3. May 14, 2017

### TSny

You need to find values of x and y so that the left-hand side and the right-hand side of v = kgxry 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?

4. May 14, 2017

### ZenMode

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

5. May 14, 2017

### patric44

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

6. May 14, 2017

### TSny

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.

7. May 14, 2017

### 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.

8. May 14, 2017

### patric44

i dont 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 :)

9. May 14, 2017

Noted.