On vacation you are traveling from New York
to California. What do you think will be true
about the flight times?
Flying west to east is (CA to NY)…
A) Slower than flying east to west
B) Faster than flying east to west
C) The same as flying east to west
If you answered B, congratulations! Flying west
to east generally takes less time than flying east
to west.
Why?
Because of
the jet stream.
Actually, there
are several jet
streams that encircle the earth: two near the equator and one
each near the Earth’s polar regions. Jet streams occur where
different air temperatures meet.
The difference in air pressure creates a body of fast-flowing
air that we call a jet stream. Due to the direction of the earth’s
spin and the fact the colder air lies to the north and warmer air
to the south, the stream flows from west to east.
Wind speeds are typically 100-150 mph during summer and
can increase to 300 mph during winter.
Questions:
1) How long would it take to fly from New
York to California (3000 miles) if you traveled
at 500 mph.
2) How long would it take to fly from
California to New York (3000 miles) if you
traveled at 600 mph.
3) Write a general equation to determine travel
time given distance and speed.
rational application - bike ride
Name_______________________________
Mr. Haas rides back and forth on the same 10 mile long road three days in a row.
Distance = 10 miles each way
On the first day there is no wind and he is able to ride at a speed of 20 mph in each
direction. On the second day there is moderate wind making him ride 2 mph faster (22
mph) in one direction and 2 mph slower (18 mph) in the other. The third day is very
windy and his speed is 5 mph faster (25 mph) one way and 5 mph slower (15 mph) on the
return.
1) On which day do you think the trip is completed in the shortest time? Why?
2) Determine the total ride time for each of the days.
Day 1: No wind effect, Day 2: Moderate wind effect, Day 3: Large wind effect
3) Determine a general equation for ride time as a function of wind effect.
4) Sketch the graph this function. Show asymptotes.
5) What is the domain of this function in the context of this problem? Explain why?
6) In terms of travel time and speed, explain the meaning of the vertical asymptote.