Question

On the earth, a stone is thrown from a height in a direction parallel to the earth’s surface while another stone is simultaneously dropped from the same height. Which stone would reach the ground first and why?

Answer 1

Answer:

1. The motion of a body with just the gravitational force acting on it is known as free fall.
2. For both stone initial velocity $u=0$, Acceleration(downward direction) = $g$
3. For both the particles, the velocity imparted is along x and not y so the initial velocity is the same (Zero) for both along y,
4. We know, $h=ut+\frac{1}{2}g{t}^2\Rightarrow 0+\frac{1}{2}g{t}^2\Rightarrow t=\sqrt{\raisebox{1ex}{$2h$}\!\left/ \!\raisebox{-1ex}{$g$}\right.}$
5. The time it took for both stones to reach the ground is $t=\sqrt{\raisebox{1ex}{$2h$}\!\left/ \!\raisebox{-1ex}{$g$}\right.}$.
6. Hence $t\propto \sqrt{h}$, time is only dependent on height, and height is the same for both particles.
7. Because the force and height are equal, they will both fall to the earth at the same moment.

Thus, Both the stones reach the ground at the same time as they are dropped from the same height and their initial velocity will be the same.