Question

Explain and justify the motion of the coin if a passenger tosses it in the upward direction while the plane is accelerating from 100 [mi/h] to 150 [mi/h].

Answer 1

A coin tossed upward by a passenger in an accelerating airplane will seem to fall straight down to the in-plane observer, but will follow a horizontal path in addition to its vertical fall to an observer on the ground, due to the plane's forward velocity.

Step-by-step explanation:

The motion of a coin tossed upward by a passenger inside an accelerating airplane is an interesting scenario highlighting principles of physics. From the in-plane observer's point of view, the coin will go up and then fall straight down if tossed vertically. This behavior is consistent with the passenger's experience due to the lack of relative motion between the coin and the airplane while it is in the air. However, for an observer on the ground, the coin participates in the plane's horizontal acceleration and velocity during its flight.

As the plane is moving from 100 mph to 150 mph, the tossed coin, when observed from outside the plane, will thus seem to follow a more horizontal path. It takes on the horizontal component of the plane's velocity in addition to the vertical motion due to gravity. Hence, two observers in different frames of reference—the plane and the Earth—would see the coin's path very differently, a concept stemming from Galilean relativity.