Question

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

Answer 1

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.

Answer 2

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.