# Rewriting the constant

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.

Related Precalculus Mathematics Homework Help News on Phys.org
rock.freak667
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:
Char. Limit
Gold Member
Err...

1 mph is not 1.67 ft/s.

1 mph is 1.467 ft/s

HallsofIvy
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.

Mentallic
Homework Helper
And there are 1000 metres / kilometre

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

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?

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

vela
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.

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?

vela
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.