What are the units of k in t = k√(h)/d²?

[Sorry!]

Question asked to find the units of k after you find the porpotionality statement



i ended up getting
$$t\propto\frac{\sqrt{h}}{d^2}$$
so i turned that into an equation and end up with
$$t=k\frac{\sqrt{h}}{d^2}$$
solved for and found it on average to be 30 now the question is asking what the units are for k... lol hmm t is in s d and h are in cm

would it be s/cm^1.5 ?? lol..

 

[symbolipoint]

Keep the corresponding units with each number. You will first obtain,
k = (t)*(d^2)/(h^0.5),

Now in that form, show the units and simplify if possible.

 

[Sorry!]

i have no idea what cm^.5 is lol

s*cm2/cm^.5 simplifies?

 

[symbolipoint]

i have no idea what cm^.5 is lol

s*cm2/cm^.5 simplifies?

Apparantly, t is in units of seconds (s);
d is in units of centimeters (cm);
h is in units of centimeters also (cm).

Not clear is do you need UNITS or DIMENSIONS.

You did not express your units with the proper exponents in your numerator. The "2" needs to be expressed as an exponent. That is the purpose of the "^" symbol.
What you have could be better simplified if needed, using laws of exponents (knowing that you have centimeter^2 as part of your numerator. How you simplify, or if you simplify no further is up to you, or depends on what is expected in your course.