Math/chemistry

Question

Covert 42.2mm/s to yrd/hour?

Answer 1

To convert units without changing the value, we use the Multiplicative Identity (that is, 1)  --  any number multiplied by 1 remains the same:

 

For this problem:

    1  =   (1000 mm) / (1 m)  =  (1 m) / (1000 mm)            [choose one of each]

    1 =  (1.094 yard) / (1 m)  =  (0.9144 m) / (1 yard)

    1  =  (60 sec) / (1 minute)  =  (1 minute) / 60 sec)

    1  =  (60 minutes) / (1 hour)  =  (1 hour) / (60 minutes)

   

 

Covert 42.2mm/s to yrd/hour?

   42.2 mm/s

   (42.2 mm/s) * 1

   (42.2 mm/s) * ((1 m)/(1000 mm)) * ((1.094 yd)/(1m)) * ((60s)/(1 min)) * ((60 min)/(1 hr))

   (42.2)*(1/1000)*(1.094/1)*(60/1)*(60/1) yd/hr     [note: mm, m, s, min cancel]

   166.20 yd/hr

Answer 2

Given: Speed in 42.2 mm/s

Find: Speed in yd/hr

 

Method:

We will have to use Dimensional Analysis to help us arrive at our answer. Be sure to set up the units so that they cancel out. Dimensional Analysis works because you are essentially multiplying the quantity by 1. 

 

Solve:

42.2 mm/s x (1 cm/10 mm) x (1 in/2.54 cm) x (1 ft/12 in) x (1 yd/3 ft) x (60 s/1 min) x (60 min/1 hr)

 

Answer:

Speed = 166 yd/hr  (Remember significant figures)