Final answer:
To find the altitude of a plane when its sonic boom reaches an observer 1.15 minutes after passing overhead, convert the time to seconds, calculate the distance the sound has traveled, and then apply the Pythagorean theorem.
Step-by-step explanation:
To calculate the altitude of a plane flying faster than the speed of sound, we need to consider the time it takes for the sonic boom to reach the observer on the ground after the plane passes overhead. The plane's speed is 1.36 times the speed of sound, which is given as 330 m/s.
First, we convert the time from minutes to seconds: 1.15 min = 1.15 × 60 s = 69 s. Next, we find the distance the sound traveled during this time: Distance = Speed × Time = 330 m/s × 69 s = 22770 m.
Now, considering the plane flies at a constant speed in a straight line and forms a right triangle where the altitude is one leg and the distance covered by sound is the hypotenuse, we can apply the Pythagorean theorem to find the altitude (h).
Let's denote the distance covered by the plane while the sound reaches the observer as 'd'. Since the plane is faster than the speed of sound, we have: d = 1.36 × 330 m/s × 69 s. After calculating d, we use the Pythagorean theorem: h^2 = d^2 - Distance^2. The altitude, h, is the square root of the result.