Final answer:
To find the height of the plane, we need to calculate the time it takes for the luggage to hit the ground and use the equation of motion. By solving the equation, we find that the distance traveled by the luggage is equal to the height of the plane. Therefore, the height of the plane is 14.34 kilometers.
Step-by-step explanation:
To find the height of the plane, we need to first calculate the time it takes for the luggage to hit the ground. We can use the equation of motion: d = vi * t + 1/2 * a * t^2, where d is the distance, vi is the initial velocity, t is the time taken, and a is the acceleration. In this case, the initial velocity is 125 m/s, the distance is unknown, and the acceleration is due to gravity and is equal to 9.8 m/s². Rearranging the equation, we have: d = 125 * t + 0.5 * 9.8 * t^2.
Next, we substitute the given time of 23.2 seconds into the equation: d = 125 * 23.2 + 0.5 * 9.8 * (23.2)^2. Solving this equation will give us the distance traveled by the luggage.
Since the luggage falls vertically, the height of the plane is equal to the distance traveled by the luggage. Therefore, once you find the distance, that will be the answer to how high the plane was.
Let's calculate the distance to find the height of the plane:
d = 125 * 23.2 + 0.5 * 9.8 * (23.2)^2
= 14340.4 meters
= 14.34 kilometers