   Chapter 3, Problem 26P

Chapter
Section
Textbook Problem

An airplane maintains a speed of 630 km/h relative to the air it is flying through, as it makes a trip to a city 750 km away to the north, (a) What time interval is required for the trip if the plane flies through a headwind blowing at 35.0 km/h toward the south? (b) What time interval is required if there is a tailwind with the same speed? (c) What time interval is required if there is a crosswind blowing at 35.0 km/h to the east relative to the ground?

(a)

To determine
The time interval for the trip if the plane flies trough a headwind blowing at 35.0km/h towards the south.

Explanation

Let positive x axis be eastward and the positive y axis be northward.

The displacement of the plane relative to the ground is,

dPG=750km due north.

The displacement of the plane relative to the air is,

dPA=(630km/h)t directed at angle α relative to the y axis.

The displacement of the air relative to the ground is,

dAG=(35.0km/h)t directed at angle β relative to the y axis.

From the vector triangle, equating the x components,

dPAsinα+dAGsinβ=0

Here,

α is the angle between dPA and dAG

β is the angle between the normal and dAG

Substitute (630km/h)t for dPA and (35.0km/h)t for dAG .

((630km/h)t)sinα+((35.0km/h)t)sinβ=0

sinα=35

(b)

To determine
The time interval for the trip if the plane flies trough a tailwind blowing at 35.0km/h .

(c)

To determine
The time interval for the trip if the plane flies trough a crosswind blowing at 35.0km/h towards the east relative to the ground.

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