Question

An airplane maintains a speed of 645 km/h relative to the air it is flying through as it makes a trip to a city 724 km away to the north.(a) What time interval is required for the trip if the plane flies through a headwind blowing at 32.1 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 32.1 km/h to the east relative to the ground?_____________h

Answer 1

(a) 1.18 h

(b) 1.07 h

(c) 1.124 h

Solution:

As per the question:

Speed of the airplane,
`v_(a) = 645\ km/h`

Speed of the wind,
`v_(w) = 32.1\ km/h`

Distance, d = 724 km

Now,

(a) To calculate time taken for the trip when the wind blows towards south:

The plane flies towards North and the wind blows towards South.

Thus the velocity of the airplane is given by:

`v = v_(a) - v_(w) = 645 - 32.1 = 612.9\ km/h`

Thus the time taken, t =
`(d)/(v) = (724)/(612.9) = 1.18\ s`

t = 1.18 h

(b) To calculate the time interval in case of the tailwind:

Now, the direction of the wind and the plane is same:

Velocity of the plane,
`v' = v_(a) + v_(w) = 645 + 32.1 = 677.1\ km/h`

Time interval, t' =
`(d)/(v') = (724)/(677.1) = 1.07\ h`

(c) To calculate the time interval in case of a crosswind:

`v`

`v`

Time taken, t" =
`(d)/(v`