An airline pilot begins a trip to duluth from an airport located 1500 km south of duluth. her air speed is 260 m/s, but a wind blows from west to east at 40 m/s that takes her off course if she flies directly north. she has the choice of heading slightly westward so that the wind causes her to end up at duluth or heading due north until she reaches a position directly east of duluth and then heading west into the wind to duluth.

which route takes a shorter time interval?

a) the first route will be shorter.
b) the second route will be shorter.
c) the routes are equal to each other.

Option A

The first route will be shorter

Explanation:

Considering the motion when the airline heads westward, the north direction speed is given by

Distance to destination is 1500 Km= 1500000 m

Time for travelling=1500000/257=5836.58 seconds

Time in minutes=5836.58/60=97.3 minutes

In case the wind sends pilot off the course

Time to travel from A to point E before heading to Duluth=1500000/260=5769.23 seconds

Time in minutes=5769.23/60=96.2 minutes

Time to travel from Westward to Duluth=Distance/speed

Distance between Westward and Duluth=40*5769.23=230769.23 m

Time to travel from Westward point  to Duluth=23769.23/(260-40)=1048.95 seconds

Time in minutes=1048.95/60=17.5 minutes

Total time taken when pilot changes course=96.2+17.5=113.7 minutes

Time difference=113.7-97.3=16.4 minutes

Therefore, the first route will be shorter .

A) The first route will be shorter

Explanation:

                 Speed =

The total distance to be covered in each case is 1500 Km= 1500000 m.

Heading westward, her air speed = 260 m/s.

So that the time required to cover the distance at that speed would be;

     Time =

              =

             = 5769.231 seconds

But if she flies directly north, a blowing wind reduces her speed. Thus speed due north, is given by;  

    =

        =  256.91 m/s

Time for traveling =

                             =

                            = 5838.621 seconds

Thus comparing the time of travel in both cases, the first route would be shorter .

  the grams     of oxygen gas   that can be produced     is 20.6   grams of o₂

calculation

2liclo₃ →   2 licl + 3 o₂

step 1:   find the moles of liclo₃

moles = mass÷ molar mass

from periodic table the molar mass of liclo₃ =6.9 +35.5   +(16 x3) =90.4 g/mol

moles=38.7 g÷90.4 g/mol=0.4281   moles

step 2:   use the   mole ratio   to calculate the moles of o2

from equation above, liclo₃: o₂   is 2: 3  

therefore the moles of   o₂=0.4281 moles x3/2 =0.6422   moles

step 3: find mass   of o₂

mass= moles x molar mass

from periodic table the   molar mass of   o₂ = 16 x2= 32 g/mol

mass=0.6422   moles   x   32 g/mol = 20.6 grams of o₂