A freely falling body weighing 2 kg is affected by a resistance force, Proportional to the speed of the body’s

A freely falling body weighing 2 kg is affected by a resistance force, Proportional to the speed of the body’s movement: Fcopr = rV, where r is the drag coefficient equal to 0.5N · s / m. What is the maximum speed of a falling body? Acceleration of gravity is considered equal to 10 m / s2

Given:

m = 2 kilograms is the mass of a free falling body;

Fsopr = r * V, where r = 0.5 N * s / m is the dependence of the air resistance force on the body speed;

g = 10 m / s2 (meter per second squared) – acceleration due to gravity (rounded off value).

It is required to determine Vmax (m / s) – the maximum speed of body movement.

By definition, the resistance force cannot be greater than the gravity force (otherwise the body would begin to move upward). That is, at the maximum value, the resistance force will be equal to the gravity force acting on the body, that is:

Fcopr = F gravity;

r * Vmax = m * g;

Vmax = m * g / r = 2 * 10 / 0.5 = 20 / 0.5 = 200/5 = 40 m / s.

Answer: the maximum body speed will be 40 m / s.