Solution to problem 13.2.19 from the collection of Kepe O.E.

Let's solve the problem:

A body with a mass of 1 kg falls vertically, the air resistance force is R = 0.03v. It is necessary to find the maximum speed of falling of the body.

Answer:

Let v be the speed of the falling body. Then the air resistance force will be equal to R = 0.03v. The force of gravity acting on the body is equal to F = mg, where m is the mass of the body, g is the acceleration of gravity.

Thus, the equation of motion of the body will look like:

mg - 0.03v = ma

where a is the acceleration of the body.

Let us express the acceleration from this equation:

a = g - 0,03v/m

Acceleration will be maximum at zero speed, i.e. when the fall begins. The maximum speed will be reached at the moment when the acceleration becomes zero:

g - 0,03v/m = 0

From here we get:

v = gm/0.03 = 327.27 m/s

Answer: 327 m/s

A solution to problem 13.2.19 from the collection of O. Kepe is proposed:

There is a body of mass 1 kg that falls vertically. The air resistance force is given R = 0.03v, where v is the speed of the body falling. It is necessary to find the maximum speed of falling of the body.

To solve the problem, we use the equation of body motion: mg - R = ma, where m is the mass of the body, g is the acceleration of gravity, R is the air resistance force, a is the acceleration of the body.

Let us express the acceleration of the body from the equation:

a = (g - R)/m

The acceleration of the body will be maximum at the beginning of the fall, when the speed is zero. The maximum speed will be reached at the moment when the acceleration becomes zero:

g - R = 0

From here we get:

v = (gm)/R = (9,811)/0.03 ≈ 327 m/s

Thus, the maximum speed of the falling body is 327 m/s. Answer: 327.

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Problem 13.2.19 from the collection of Kepe O.?. consists in determining the maximum falling speed of a body weighing 1 kg, taking into account the force of air resistance, which depends on the falling speed and is equal to R = 0.03v. The answer to the problem is 327.

To solve the problem, it is necessary to use the equation of motion of the body, which describes the change in speed over time:

mdv/dt = mg - Rv

where m is the mass of the body, g is the acceleration of free fall, v is the speed of fall, R is the force of air resistance.

To find the maximum speed of a falling body, you need to find the speed value at which the acceleration becomes zero:

mg - R*v_max = 0

It follows that the maximum fall speed is v_max = mg/R = 10*9.81/0.03 ≈ 327 m/s.

Thus, to solve a problem, it is necessary to know the equation of motion of a body and the ability to apply it to solve specific problems, taking into account the available data and conditions.

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