Question

3. The doctor notices that Janet has long fingernails, and comments that fingernails grow at a rate (or

speed) of 2.50 cm / year. Convert this speed to kilometers / second. Show your work. (6 pts)

Answer 1

7.93 × 10⁻¹³ km/s

Step-by-step explanation:

Step 1: Given data

Rate of growth of the fingernails (r): 2.50 cm/year

Step 2: Convert "r" from cm/year to km/year

We will use the following conversion factors.

• 1 m = 100 cm

• 1 km = 1000 m

`(2.50cm)/(year) * (1m)/(100cm) * (1km)/(1000m) = 2.50 * 10^(-5) km/year`

Step 3: Convert "r" from km/year to km/s

We will use the following conversion factors.

• 1 year = 365 day

• 1 day = 24 h

• 1 h = 60 min

• 1 min = 60 s

`(2.50 * 10^(-5) km)/(year) * (1year)/(365day) * (1day)/(24h) * (1h)/(60min) * (1min)/(60s) = 7.93 * 10^(-13) km/s`

2.50 cm/year is equal to 7.93 × 10⁻¹³ kilometers/second.