You hear the sonic boom of a high-speed jet plane exactly 3.10 s after it passes directly overhead in level flight. At the time you hear the boom, you see the plane at an angle of 22.0 o above the horizon. Assume that the speed of sound at the altitude of the plane is 325 m/s.

How fast is the plane traveling?

d = 325m/s * 3.10s = 1008 m. = Hor. distance traveled by sound.

d = 1008/Cos22 = 1087 m.
V = 1087m/3.1s = 350.5 m/s. = Speed of the plane.

To determine the speed of the plane, we can first find the distance between the observer and the point directly underneath the plane when the sonic boom is heard. Then we can use the time it took for the sound to reach the observer to calculate the distance the plane traveled in that time.

To find the distance between the observer and the point directly underneath the plane, we can use trigonometry. Since we know the angle of 22.0 degrees and the height of the observer is essentially constant, we can use the tangent function:

tan(22.0 degrees) = height of observer / distance to point underneath the plane

Let's call the distance to the point underneath the plane "x". Rearranging the equation, we get:

x = height of observer / tan(22.0 degrees)

Now, to find the distance the plane traveled, we can use the speed of sound and the time it took for the sound to reach the observer. The speed of sound is given as 325 m/s and the time delay is given as 3.10 seconds. Using the formula:

distance traveled = speed of sound * time delay

we can calculate the distance traveled.

Finally, to find the speed of the plane, we divide the distance traveled by the time delay:

speed of plane = distance traveled / time delay

By plugging in the values and calculating, we can find the speed of the plane.