2. An airplane flies horizontally at a constant speed, piloted by rescuers who a

Question

2. An airplane flies horizontally at a constant speed, piloted by rescuers who are searching for a disabled boat. When the plane is directly above the boat, the boat's crew blows a loud horn. By the time plane's sound detector receives the horn's sound, the plane has traveled a distance equal to one-half its altitude above the ocean. (The speed of sound is 343 m/s.) If it takes the sound 4.00s to reach the plane, determine

a) the altitude of the plane, and

b) its speed, in m/s. What is its speed in knots (nautical miles per hour)?

Explanation / Answer

Distance travelled by sound = 343*4 = 1372 m

So the hypotaneous of the triangle is 1372 m

Let the altitue be h

The distance travelled by plane be h/2

a) h^2 + (h/2)^2 = 1372^2

h = 1227.154 m

b)During 4 sec the plane travels h/2 so speed

= (1227.154/2) / 4

=153.39 m/sec

[1 m/sec = 1.943 knots]

=298.17 knots

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