# What will be the answer?

## . A train is moving forward at a velocity of 2.0 m/s. At the instant the train begins to accelerate at 0.80 m/s2, a passenger drops a quarter which takes 0.50 s to fall to the floor. Relative to a spot on the floor directly under the quarter at release, it lands: (A) 1.1 m toward the rear of the train. (B) 1.0 m toward the rear of the train. (C) 0.10 m toward the rear of the train. (D) directly on the spot. (E) 0.90 m toward the front of the train.

Aug 4, 2018

Option $C$ is the answer

#### Explanation:

Due to inertia of motion the quarter at the time of its release will have same velocity as that of the train i.e.$2 m \text{/} s$. As the time of fall is $0.5 s$ it will move $2 \times 0.5 = 1 m$ towards the front of the train during its time of flight.

But the train will move with acceleration $0.8 m {s}^{-} 2$ and will move during the time of fall of the quarter by the distance $= 2 \times 0.5 + \frac{1}{2} \times 0.8 \times {\left(0.5\right)}^{2} = 1.1$ m
Hence the quarter will fall $0.1 m$ toward the rear of the train relative to the spot directly under the quarter at release.

Option $C$ is the answer