Solution of problem D1 Option 20 Dievsky V.A. Malysheva IA

Solution to problem D1 B 20. Let us assume that the vertical descent of a parachutist of mass m occurs without an initial speed from a height of h = 200 m. In this case, we take into account the presence of air resistance force, which is proportional to the square of the speed, R = 3mv2. It is necessary to determine the speed of the parachutist at the moment of landing.

The solution to this problem can be found by considering the laws of conservation of energy and motion. The skydiver is in a state of free fall, so his acceleration will be equal to the acceleration of free fall g = 9.8 m/s². At the same time, we take into account that the force of air resistance is directed upward.

Using the law of conservation of energy, we can write that the potential energy of a parachutist at height h is equal to his kinetic energy at the moment of landing. Thus, mgh = (mv²)/2, where m is the mass of the parachutist, v is his speed at the moment of landing.

Next, taking into account the force of air resistance, we can write down the equation of motion of the parachutist: m(dv/dt) = mg - R, where t is the time that has passed since the beginning of the descent.

Having solved this differential equation, we find the speed of the parachutist at the moment of landing: v = sqrt(mg/R)*sqrt(1 - exp(-2Rt/m)).

Thus, knowing the parachutist’s mass, altitude, air resistance and descent time, one can determine his speed at the moment of landing.

We present to your attention a digital product - Solution to problem D1 Option 20, written by V.A. Dievsky. and Malysheva I.A.

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The solution to the problem was carried out by professionals in their field and meets all the requirements and standards established for this level of education.

By purchasing our digital product, you receive a complete solution to the problem, which you can use to independently study the material, prepare for exams, or test your knowledge.

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We present to your attention a digital product - Solution to problem D1 Option 20, written by V.A. Dievsky. and Malysheva I.A. This product is a solution to a specific problem in the field of mathematics, namely, theoretical mechanics.

The task is to determine the speed of a parachutist at the moment of landing during a vertical descent without an initial speed from a height of 200 meters in the presence of an air resistance force proportional to the square of the speed.

The solution to the problem was carried out by professionals in their field and meets all the requirements and standards established for this level of education. By purchasing this product, you receive a complete solution to the problem, formatted in Word or as a handwritten solution, which can be used to independently study the material, prepare for exams, or test your knowledge.

In addition, the product contains beautiful HTML design, which makes it convenient and easy to use. Immediately after payment you will receive a link to the archive with the solution to the problem on theoretical mechanics D1 B20 (condition 20) from the collection of tasks “Theoretical Mechanics” Dievsky V.A., Malysheva I.A. 2009 for university students.

When purchasing this product, we hope that it will help you successfully understand this problem and gain the necessary knowledge in the field of theoretical mechanics.

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For sale is the solution to problem D1 Option 20 from the collection of tasks "Theoretical Mechanics" Dievsky V.A., Malysheva I.A. Description of the problem: a vertical descent of a parachutist with a mass m occurs without an initial speed from a height of h = 200 m in the presence of an air resistance force proportional to the square of the speed, R = 3mv2. As a result of the purchase, you will receive a link to an archive with a solution to the problem, formatted in Word (handwritten solution or typed in Word) and packed in a zip archive, which will open on any PC. After checking the solution, the author will be pleased if you leave positive feedback.

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