The body falls freely from a height of 2 km. How fast will it fall to the ground?

When solving the problem, let us assume that the acceleration of gravity along the entire path is the same and equal to g = 9.81 m / s2, and also other forces do not act on the body besides the gravitational force.

The motion of the falling body is uniformly accelerated with acceleration g. If the initial speed of the body is zero, then its speed and the distance traveled change according to the laws:

v (t) = g * t;

s (t) = g * t ^ 2/2.

In a fall, the path traveled by the body is equal to the height of the rise; then you can write:

h = g * t ^ 2/2,

whence the fall time is

t = √ (2 * h / g).

Then the speed with which the body falls to the ground is equal to

v = g * √ (2 * h / g) = √ (2 * g * h);

v = √ (2 * 9.81 * 2000) = 198 m / s.