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 you
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Question 828543: 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 200 mph and an altitude of 3,000 feet, and you hear the sound at what seems to be an angle of inclination of 20 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 200 mph and an altitude of 3,000 feet, and you hear the sound at what seems to be an angle of inclination of 20 degrees.
At what angle should you actually look in order to see the plane?
Assume the speed of sound is 1,100 ft/sec
:
Draw a diagram showing the two right triangles formed by this problem
One where sound originate from and one where the plane is now
:
since we will be dealing in seconds, find the speed of the aircraft in ft/sec = 293.3 ft/sec
:
Find the slant range to the point where the sound originated
That will be the hypotenuse of a right triangle formed with ground and
the height of the aircraft (3000')
sin(20) =
h = 8771.4 ft
Find how long it will take the sound to travel this distance at 1100 ft/s = 7.974 sec
Find how far the aircraft will travel in 7.974 sec
7.874 * 293.3 = 2338.8 ft towards you
:
Now we are dealing with a new right triangle, find the distance from you to
a point below where the aircraft is now
Using the original triangle find the distance below the original point
cos(20) =
d = 8771.4 * cos(20)
d = 8242.4 ft
Find the distance to the point below the aircraft now
8242.4 - 2338.8 = 5903.6, (subtracted the distance the aircraft traveled)
Find the new angle (A) using the above and 3000ft
ArcTan(A) =
A = 26.94 degrees, the angle to where the plane is now
