Verify that the coin dropped by the airline passenger in the Example 3.8 travels 144 m horizontally while falling 1.50 m in the frame of reference of the Earth.

Example 3.8:

An airline passenger drops a coin while the plane is moving at 260 m/s. What is the velocity of the coin when it strikes the floor 1.50 m below its point of release: (a) Measured relative to the plane? (b) Measured relative to the Earth?

Figure 3.50 The motion of a coin dropped inside an airplane as viewed by two different observers. (a) An observer in the plane sees the coin fall straight down. (b) An observer on the ground sees the coin move almost horizontally.

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We need to verify the horizontal distance travelled by the coin is .

Using the kinematics equation the vertical distance travelled by the coin is

Where

is the final vertical position of the coin

is the time taken by the coin to reach down from the initial position.

is the initial vertical position of the coin and it is zero.

So