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A high-performance jet plane, practicing radar avoidance ma- neuvers, is in horizontal flight 35 m above the level ground. Suddenly, the plane encounters terrain that slopes gently up- ward at 4.3°, an amount difficult to detect; see Fig. How much time does the pilot have to make a correction if the plane is to avoid flying into the ground? The airspeed is 1300 km/h

A high-performance jet plane, practicing radar avoidance ma- neuvers, is in horizontal flight 35 m above the level ground. Suddenly, the plane encounters terrain that slopes gently up- ward at 4.3°, an amount difficult to detect; see Fig. How much time does the pilot have to make a correction if the plane is to avoid flying into the ground? The airspeed is 1300 km/h

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
8 years ago
Given:

Inclination of slope,\o = 4.3^{\circ} .
Altitude of plane, h = 35.
Speed of air, vair = 1300 km/h.
Let us assume that the length of slope to the point where the plane meets the slope is given by length l. Also, the speed of the plane is equal in magnitude with that of the speed of air, therefore the speed of the plane (say vplane)is equal to 1300 km/h.
The figure below shows the motion of the plane and various other variables.


236-145_fish.JPG

From the figure one can see that the altitude (say d) of the slope is given in terms of length l of slope and the angle \oas:
d = l sin \o
If the plane were to collide with the slope then the following condition should be fulfilled:
h-d = 0
d = h
Substitute the value of d and h to have
236-139_l.JPG
Therefore the length of the slope after which the plane collides is 466.7 m
Now, to calculate the horizontal distance (say x) that the plane will travel if it collides with the slope, we calculate the base of triangle ABC as
From triangle ABC, we have
x = l cos \o
Substitute the value of l and \o, to have
x = (446.7m) cos (4.3°)
= 465.3m
Therefore the horizontal distance at which the plane will collide with the slope is 465.3 m.
The time (say t)that the plane had before it run into the inclined ground ahead is given as:
t = \frac{x}{v_{plane}}
Substituting the value of x and vplane to have

236-1430_456.JPG

Rounding off to two significant figures

t = 1.3 s

Therefore the plane has 1.3 s before it will run into the ground, and avoid the collision.

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