A boy standing on a long railroad car throws a ball straight upwards. the car is moving on the horizontal road with an acceleration of $1{\text{m/s}}^2$ and the projection speed in the vertical direction is $9.8\text{m/s}$. How far behind the boy will the ball fall on the car ?

The correct option is B 2 m
Let the initial velocity of car be ${}^{\prime }{u}^{\prime }$.
Time of flight, $t=\frac{2u_y}{g}=2$
where $u_y=$ component of velocity in vertical direction
Distance travelled by car $x_c=u\times 2+\frac{1}{2}\times 1\times 2^2=2u+2$
Distance travelled by ball $x_b=u\times 2$ (Since it has no acceleration in $x$-direction)
$x_c-x_b=2u+2-2u=2\text{m}$