Question

What is faster, up or down?

A ball of dough ?? = 1 kg is thrown vertically upwards from the surface of the
Earth, with a positive initial velocity ??0 = 20 m / s. Suppose the forces acting
on the ball are gravity and a retarder of air resistance, with opposite direction
to that of the movement.
2._ If the retarding force is proportional to the instantaneous velocity, use the second law of
Newton to determine an equation that describes the situation and use it to calculate the velocity and
position in every moment. Then determine the time for the maximum the maximum height will be reached, and the
time from its maximum height until it hits the ground, (consider the constant of
proportionality equal to 0.1 Ns / m) do these times coincide? What would be your conclusion now with
Regarding whether it takes longer to go up or down.
3._ Newton in his Mathematical Principle, considered the retarding force as proportional to the
square of the instantaneous speed, perform the previous exercise taking into account this
consideration.
4._ Empirical research indicates that the actual dependence of air resistance on
speed can be quite complicated. In many cases it is enough to assume the force
retarder is ???? = ??????, where 1 ≤ ?? ≤ 2, velocity instantaneous velocity and one is a constant of
proportionality, which depends on the size and shape of the body, as well as the density and
air viscosity In general, ?? = 1 is used for low speeds and ?? = 2 for
high speeds, while 1 <?? <2, for intermediate speeds. Note that at the point
2 the value of 1 is 1, while at point 3 the value of ?? is 2.
Choose a value for ??, 1 <?? <2, to describe the situation as in point 2, and solve the
equation to find the instantaneous velocity 5 seconds later. You may use a
numerical method for the solution, in that case specify the reason for choosing the method

Answer 1