Converting Velocity from mph to ft/s: How to Rewrite a Constant Formula

[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.

 

[rock.freak667]

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.

 

[Char. Limit]

Err...

1 mph is not 1.67 ft/s.

Spoiler

1 mph is 1.467 ft/s

 

[HallsofIvy]

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]

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.

 

[vela]

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?

 

[vela]

The units of \sqrt{h}, if h is in feet, is ft^1/2, which cancels with the ft^1/2 in the denominator of the units of the constant. The units of v is mph, so the what's left over after the ft^1/2 cancels must be miles/hr.

If you want the formula to give an answer in ft/s, the constant needs to have units of ft/(s ft^1/2).

 

[Ryuk1990]

I got 8.02 as the new constant. Is that right?