Air Plane In Flight - Head Wind Tail Wind
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Air Plane In Flight - Head Wind Tail Wind

An airplane can fly at a speed of 200 miles/hr in still air. It can fly a distance of 800 miles with tail wind (wind is in same direction as direction of flight). It can fly 640 miles with head wind (wind is against direction of flight). What is the speed of the wind?

The string:
(a) S7P5A51 (Physical Change - Speed).
The math:

Pj Problem of Interest (PPI) is of type change. Problems of speed, velocity, acceleration and duration are associated with motion, they are generally Pj Problems of the type change because the PPI addresses rate of change.
Figure 4.1 illustrates the directions of the head wind and tail wind. Sometimes the vertical component of the wind is not zero. Such a wind is called a cross wind and it has both a vertical and horizontal components.
Let speed of the wind be w:
Then, speed of airplane with tail wind = 200 + w
Speed of airplane with head wind = 200 - w
So, (200 + w)t = 800 ----(1) (t is time in hrs).
Also, (200 - w)t = 640 ----(2)
Solving equations (1) and (2) simultaneously gives:
400t = 1440
So, t = 18/5 hrs
Substituting t in equation (1) or equation (2), gives:
The speed of the wind, w = 22 miles/hr.

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