SOLUTION: An object with mass 21kg is in free fall. It has two forces acting on it: gravity and air resistance. For this model we will take the ground to be at height 0, the height of the ob

Question 1184652: An object with mass 21kg is in free fall. It has two forces acting on it: gravity and air resistance. For this model we will take the ground to be at height 0, the height of the object to be y(t) meters from the ground, and the acceleration due to gravity to be −9.81ms^(2).
We want to set up a differential equation for the forces acting on the object. The force due to gravity is is given by mass times acceleration acting in the opposite direction of y. The force due to air resistance is proportional to the square root of the velocity of the object in the same direction is y. The constant of proportionality for the wind resistance has been measured at 0.55. Find the differential equation that models the displacement of the object y at time t.
My answer is -9.81+(0.55/21)sqrt(y')=0 , wrong.
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

I confirm that your answer is wrong.

        Your post contains SEVERAL ERRORS.

One error is that the resistance force is proportional to the square root of the velocity.

In Engineering, the resistance force is usually taken as proportional to the SQUARE of the velocity.

As a reference, see, for example, this source,
https://www.sciencedirect.com/topics/mathematics/resistive-force

in a long row of other similar sources.

So, in fact, the correct equation for forces would be

         - = .     <<<---===   the right side is the force providing acceleration . . .

In this equation, you may choose the signs in other way, taking into account the directions of forces and y-axis ---

I leave it on your consideration.

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