A jetliner travels with a constant speed of 597.4 km/h relative to the air to a city 780.1 km due south.
(a) What is the time interval required to complete the trip if the jetliner is experiencing a headwind of 41.1 km/h toward the north?
h
(b) What is the time interval required to complete the trip if the jetliner now experiences a tailwind of the same speed?
h
(c) What is the time interval required to complete the trip if the jetliner now experiences a crosswind of the same speed relative to the ground towards the west? (Enter your answer to at least three decimal places.)
h
the jet's velocity vector is v=<0,-597.4>
(a) the headwind is w=<0,41.1>
v+w = <0,-556.3>
since time = distance/speed, it is 780.1/556.3 = 1.4 hrs
Now do the others the same way, adding vectors to get the final velocity vector. Then the speed is the magnitude of that vector.
a. V*t = 780.1.
(597.4-41.1)*T = 780.1
T = 1.4 hrs.
b. (597.4+41.1)*T = 780.1.
T = ?.
c. (-41.1-597.4i)*T = 780.1
V = sqrt(41.1^2+597.4^2) = 598.82,
598.82*T = 780.1,
T = 1.303 hrs.
To find the time interval required for the jetliner to complete the trip in each scenario, we need to use the formula:
Time = Distance / Speed
(a) With a headwind of 41.1 km/h towards the north:
The speed of the jetliner relative to the ground would be:
Speed = Jetliner's airspeed - Headwind speed
Speed = 597.4 km/h - 41.1 km/h = 556.3 km/h
The distance traveled is 780.1 km.
So, the time interval required is:
Time = Distance / Speed
Time = 780.1 km / 556.3 km/h
Time ≈ 1.400 hours (rounded to three decimal places)
Therefore, the time interval required to complete the trip with a headwind of 41.1 km/h is approximately 1.400 hours.
(b) With a tailwind of the same speed (41.1 km/h):
The speed of the jetliner relative to the ground would be:
Speed = Jetliner's airspeed + Tailwind speed
Speed = 597.4 km/h + 41.1 km/h = 638.5 km/h
Using the same distance (780.1 km), the time interval required is:
Time = 780.1 km / 638.5 km/h
Time ≈ 1.221 hours (rounded to three decimal places)
Therefore, the time interval required to complete the trip with a tailwind of 41.1 km/h is approximately 1.221 hours.
(c) With a crosswind of the same speed (41.1 km/h) towards the west:
The crosswind does not affect the jetliner's speed along the southward direction. As a result, the previous speed remains the same:
Speed = 597.4 km/h
Using the same distance (780.1 km), the time interval required is:
Time = 780.1 km / 597.4 km/h
Time ≈ 1.305 hours (rounded to three decimal places)
Therefore, the time interval required to complete the trip with a crosswind of 41.1 km/h towards the west is approximately 1.305 hours.