Final answer:
The horizontal distance traveled by the coin dropped by the airline passenger is approximately 144 m.
Step-by-step explanation:
In example 3.8, the observer on the ground sees the coin move almost horizontally while falling 1.50 m.
To determine the horizontal distance traveled by the coin, we can use the formula: distance = velocity x time.
Since the coin falls vertically, the time it takes to fall is the same as the time it takes to travel horizontally.
Therefore, if we can determine the time it takes for the coin to fall 1.50 m, we can use that time to calculate the distance traveled horizontally.
In the vertical direction, we can use the formula H = (1/2)gt^2, where H is the vertical distance, g is the acceleration due to gravity, and t is the time. Substituting the given values, we have: 1.50 = (1/2)(9.8)t^2.
Solving for t, we find t = sqrt(1.50/4.9) = 0.553 s. Since the horizontal velocity is constant, we can use the formula distance = velocity x time.
The velocity is not explicitly given, but since we are in the frame of reference of the Earth, we can assume the initial horizontal velocity of the coin is the horizontal velocity of the plane before the coin is dropped, which is 260 m/s.
Therefore, the horizontal distance traveled by the coin is approximately 260 m/s x 0.553 s = 143.38 m, which is close to 144 m.
Therefore, option (c) 140 m is the closest approximation to the horizontal distance traveled by the coin.