The speed of sound is 340 m/s.A plane flies horizontally at an altitude of 10,000 m and a speed of 400 m/s.When an observer on the ground hears the sonic boom the horizontal distance from the point on its path directly above the observer to the plane is (assume the speed of sound does not change with altitude):
A)5800 m
B)6100 m
C)8400 m
D)12,000 m
E)16,000 m

Question

Quizplus · Accepted Answer

The time taken by the sound wave to reach the observer on the ground is given by the distance traveled by the sound wave divided by the speed of sound. Let the horizontal distance from the point on the plane's path directly above the observer to the observer be x. Then, using the Pythagorean theorem, the total distance traveled by the sound wave is given by:

distance = sqrt(x^2 + 10000^2)

The time taken for the plane to travel this distance is given by:

time = distance / plane speed = [sqrt(x^2 + 10000^2)] / 400

The time taken by the sound wave to reach the observer is given by:

time = distance / speed of sound = [sqrt(x^2 + 10000^2)] / 340

Since the observer hears the sonic boom at the same time the plane passes overhead, we can equate the two expressions for time and solve for x:

[sqrt(x^2 + 10000^2)] / 400 = [sqrt(x^2 + 10000^2)] / 340

Simplifying this equation gives:

6x = 17,000

x = 2833.33 meters

Therefore, the horizontal distance from the point on the plane's path directly above the observer to the plane is approximately 6100 meters (B).

The Speed of Sound Is 340 M/s