Question

An airplane maintains a speed of 687 km/h relative to the air it is flying through as it makes a trip to a city 780 km away to the north. (Assume north is the positive y-direction and east is the positive x-direction.)

(a) What time interval is required for the trip if the plane flies through a headwind blowing at 36.6 km/h toward the south?

________h

(b) What time interval is required if there is a tailwind with the same speed?
_______h

(c) What time interval is required if there is a crosswind blowing at 36.6 km/h to the east relative to the ground?
_______ h

Answer 1

here,

the airplane speed , v1 = 687 km/h j

s = 780 km j

a)

the speed of wind , v2 = 36.6 km/h (-j)

the time taken , t = s /(v1 + v2)

t = 780 / ( 687 - 36.6) h

t = 1.2 h

b)

when

the speed of wind , v2 = 36.6 km/h (j)

the time taken , t = s /(v1 + v2)

t = 780 / ( 687 + 36.6) h

t = 1.08 h

c)

when wind is traveling to the east

let the speed of plane be v

36.6 = 687 * sin(theta)

theta = 3.05 degree

the time taken , t = s /( v1 * cos(theta) )

t = 780 / ( 687 * cos(3.05)) = 1.14 h