# Rewriting the constant

Ryuk1990
Ok, here is a certain formula and I have to change it.

V = 5.47$$\sqrt{h}$$

V is velocity in mph while h is distance in ft.

I need to determine a new constant so that V is in feet per second. How do I go about doing that? Do I just convert V first and then take the constant and multiply it by the numbers that I needed to convert to ft/s?

By the way, h stays the same as just ft.

## Answers and Replies

Homework Helper
If 1 mph is 1.67 ft/s (recheck this for me)

How much ft/s is V mph?

EDIT: As Char. Limit says, 1mph is 1.467 ft/s

I forgot a 4 it seems.

Last edited:
Gold Member
Err...

1 mph is not 1.67 ft/s.

1 mph is 1.467 ft/s

Homework Helper
There are 5280 ft/mi. There are 60 sec per minute and 60 minutes per hour and so 3600 seconds per hour.

1 mi/hr= (1 mi/hr)(5280 ft/mi)/(60 sec/hr)= 5280/60 (mi/hr)(ft/mi)(hr/sec= 1.47 ft/sec.

Homework Helper
And there are 1000 metres / kilometre

I dunno... metric units just seem simpler...

Ryuk1990
Yeah I know how to convert but I'm asking how do I change the constant 5.47 in the formula to accommodate V in ft/sec? Do I just multiply 5.47 by the numbers that I multiplied into V to convert it?

CescGoal
I believe you would just multiply the equation the same way HallsofIvy has done; it's called the Grid Method.

Staff Emeritus
Homework Helper
Ok, here is a certain formula and I have to change it.

V = 5.47$$\sqrt{h}$$

V is velocity in mph while h is distance in ft.

I need to determine a new constant so that V is in feet per second. How do I go about doing that? Do I just convert V first and then take the constant and multiply it by the numbers that I needed to convert to ft/s?

By the way, h stays the same as just ft.
Just put the units in explicitly:

$$v=5.47 \frac{\mbox{miles}}{\mbox{hr ft}^{1/2}}\sqrt{h}$$

and convert the units on the constant like you normally do.

Ryuk1990
Just put the units in explicitly:

$$v=5.47 \frac{\mbox{miles}}{\mbox{hr ft}^{1/2}}\sqrt{h}$$

and convert the units on the constant like you normally do.

I have no idea how you got that unit for the constant.

I also don't know what you mean by converting the units on the constant like you normally would. Convert the units on the constant into what?

Staff Emeritus
The units of $\sqrt{h}$, if h is in feet, is ft1/2, which cancels with the ft1/2 in the denominator of the units of the constant. The units of v is mph, so the what's left over after the ft1/2 cancels must be miles/hr.