Question

An object is dropped from the window of a train moving horizontally with a uniform speed from a height 2.45 m above the ground. What is the time taken by the object to reach the ground?

Answer 1

Taking the y-direction vertically downwards,
Initial velocity along the y-direction, $u=0$
Displacement along the y-direction, $h=2.45m$
Acceleration along the y-direction, $a=g=9.8m/s^2$

Using the second equation of motion,
$s=ut+\frac{1}{2}a{t}^2\Rightarrow 2.45=\frac{1}{2}\times 9.8\times t^2\Rightarrow t^2=\frac{1}{2}\Rightarrow t=\frac{1}{\sqrt{2}}=0.707sec$