SOLUTION: It is a common experience to hear the sound of a low flying airplane, and look at the wrong place in the sky to see the plane. Suppose that a plane is traveling directly toward yo

Question 1103846: It is a common experience to hear the sound of a low flying airplane, and look at the wrong place in the sky to see the plane. Suppose that a plane is traveling directly toward you at a speed of 220 mph and an altitude of 1,600 feet, and you hear the sound at what seems to be an angle of inclination of 26 degrees.
At what angle should you actually look in order to see the plane? Assume the speed of sound is 1,100 ft/sec
Thank you in advance for you help!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
It is a common experience to hear the sound of a low flying airplane, and look at the wrong place in the sky to see the plane.
Suppose that a plane is traveling directly toward you at a speed of 220 mph and an altitude of 1,600 feet, and you hear the sound at what seems to be an angle of inclination of 26 degrees.
At what angle should you actually look in order to see the plane? Assume the speed of sound is 1,100 ft/sec.
:
Find the distance to plane where the sound originated. That is the hypotenuse (h) of a right triangle:
Use the sine of 26 degrees
sin(26) =
h =
h = 3650 ft
:
Find how long it take sound to travel 3650 ft
= 3.32 seconds
:
Find how far the plane travels in 3.32 sec at 220 mph
The plane travels = 1071.25 ft
:
Find the distance (d) to the point directly below the point of origin of the sound of the plane.
Use tangent of 26 degree
tan(26) =
d =
d = 3280.5 ft
Find the distance to the point below the airplane after 3.32 sec
3280.5 - 1071.25 = 2209.25 ft
:
Find the angle (A) to the where the plane actually is after 3.32 sec
tan(A) =
A = 35.9 ~ 36 degrees is the angle where you should see the plane

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