Question

Suppose your hair grows at the rate of 1/36 inches per day. Find the rate at which it grows in nanometers per second. Because the distance between atoms in a molecule is on the order of 0.1 nm, you answer suggests how rapidly layers of atoms are assembled in this protein synthesis. Your units should be "atomic layers/sec"

Answer 1

hair grows at rate of 8.166 nm/s

Step-by-step explanation:

given data:

grow rate= (1/36)in/day

we know that

1 day = 86400 seconds

therefore we have
`= (1)/(36)inc / 86400 sec`

first change equation to
`(1)/(36)inc / 86400 sec.`

Then you find x in/s
`= (1)/(36)inc / 86400 sec`

`x/s = (1)/(36)inc / 86400 sec`

`(86400s)x = ((1)/(36)inc) s`

`x = ((1)/(36)\ inc)/(86400) = 3.21 x 10^(-7) in/second`

Now convert in/sec into meters/second.

we know that 1m = 39.37in

`x/1m = (3.21 x10^(-7) in)/(39.37\ in)`

`(39.37in)x = (3.21 *10^(-7) in) m`

`x = (3.21 * 10^(-7))/(39.37)m`

x =
`8.166 * 10^(-9)` m/second

Now convert
`8.166 * 10^(-9)` m/second into nm/second

we know that
`1nm = 10^(-9)m`

`x/nm = (8.166x 10^(-9) m/second)/(10^(-9) m)`

x =8.166 nm/second

therefore hair grows at rate of 8.166 nm/s