Question

A train is standing on a platform, a man inside a compartment of a train drops a stone. At the same instant the train starts with constant acceleration. What is the path of stone as seen by the person who drops the stone is:
A. Parabola
B. Straight line for some time and parabola for the remaining time
C. Straight line
D. Variable path that cannot be defined

Answer 1

Hint: The person inside the train will see the stone moving in opposite direction of the train since train is moving with a constant acceleration and he is in a accelerated frame of reference and the stone will experience a pseudo acceleration with respect to the boy inside the train.

Complete step by step answer:
Since the initial velocity of the stone is zero with respect to man. So when the ball is dropped, the the ball has two accelerations. One in the downward direction .i.e. gravity and one is the pseudo acceleration i.e. in the negative direction of motion of the train. So the distance travelled by the train in downward direction is,

$y = \dfrac{1}{2}g{t^2}$
$\dfrac{y}{g} = \dfrac{1}{2}{t^2}$ …… (I)

Here, y is the downward distance travelled, g is the acceleration due to gravity and t is the time.

The distance moved by the stone in horizontal direction is,

$x = \dfrac{1}{2}a{t^2}$
$\dfrac{x}{a} = \dfrac{1}{2}{t^2}$ …… (II)
Here, x is the horizontal distance, a is the acceleration and t is the time.

On comparing equations (I) and (II),

$\begin{array}{l}
\dfrac{y}{g} = \dfrac{x}{a}\\
y = \dfrac{g}{a}x
\end{array}$

Let $\dfrac{g}{x} = C$ where C is a constant so,
$y = C\,x$

Here this is the equation of a straight line.

So, the correct answer is “Option C”.

Note:
The stone as seen by the observer standing on the ground is parabola. Because he will only see the ball falling downwards and the equation of the trajectory of the ball will be parabola as displacement would be proportional to square of the time.