A jet starts of at a point A and is flying horizontally. And person is standing at a point B on the ground which is to the right of point A. When the jet is directly over the person, the person hears sound coming from point A. The average air temp is 20 deg C. If the speed of the plane at A is 164m/s, what is its speed at B, assuming constant acceleration? The angle between point A and the line of sight of the person on the ground is 36 deg.

Question

A jet starts of at a point A and is flying horizontally. And person is standing at a point B on the ground which is to the right of point A. When the jet is directly over the person, the person hears sound coming from point A. The average air temp is 20 deg C. If the speed of the plane at A is 164m/s, what is its speed at B, assuming constant acceleration? The angle between point A and the line of sight of the person on the ground is 36 deg.

Answer 1

Let X be the horizontal distance from A to the point above B. Let Vs be the sound speed and Vb be the plane's velocity at point B.

The time required for the plane to fly the distance X is 2X/(164 + Vb), assuming constant acceleration, since (Vb+164)/2 is the average velocity. That equals the time required for the sound to go from A to B, which is X/(Vs*cos36)
Therefore
2/(164+Vb) = 1/Vs*cos36
0.809 Vs = 82 + Vb/2
Vb = 1.608 Vs -168
The sound speed is Vs = 343 m/s, so
Vb = 383 m/s
That is a lot of accleration, going from mach 0.5 to about 1.1

Answer 2

Angle's actually 56 degrees...

Answer 3

To find the speed of the jet at point B, we can use the concept of constant acceleration and the relationship between distance, time, initial velocity, acceleration, and final velocity.

Let's break down the problem step by step:

Step 1: Find the distance between the jet and the person at point B.
Since the person hears the sound when the jet is directly over them, the distance between the jet and the person at point B is the horizontal distance between point A and B. However, we don't have the value of this distance in the question. Therefore, we will need to use additional information to find this distance.

Step 2: Find the time it takes for the sound to reach the person at point B.
We know that sound travels at a speed of approximately 343 m/s in air at 20 degrees Celsius. Therefore, we can use this information and the distance between point A and B to calculate the time it takes for the sound to reach the person.

Step 3: Find the time it takes for the jet to reach point B after being directly above the person.
Since the jet is moving horizontally at a constant acceleration, we can use the definition of average acceleration to find the time it takes for the jet to reach point B from the moment it is directly above the person.

Step 4: Find the final velocity of the jet at point B.
Using the equation of motion that relates final velocity, initial velocity, acceleration, and time, we can calculate the final velocity of the jet at point B.

Now, let's calculate each step:

Step 1: Since we don't have the distance between point A and B, we cannot proceed further with the calculation. Please provide the distance between point A and B, or any additional information that can help determine this distance.