For an object moving vertically in air under gravity and experiencing a drag for

Question

For an object moving vertically in air under gravity and experiencing a drag force proportional to the square of the object's speed (drag force = 1/2 * cd * air density * cross sectional area * v^2 , where the coefficient of drag cd = 0.5, air density = 1.2). Objects are dropped from from rest from a 100-meter tall building. Let mass = 0.145 kg and radius = 0.0366. Plot height, speed, acceleration versus t, or simply give equations to express the functions height versus time y(t), speed versus time v(t), and acceleration versus time a(t).

Explanation / Answer

F=mg - 1/2*cd**A*v2

h initial=100m

cd = 0.5

m=0.145 kg

r =0.0366 m

A=r2 = 4.2 * 10-3 m2

= 1.2 kg/m3

1/2*cd**A = 1.26*10-3

mg=.45*9.8 = 4.41

F= mg - 1.26*10-3 * V2 = m dv/dt -----(1)

above expression which is in the form of-

mg - cx^2 = mdx/dt

integrating this-

you get the expression for velocity w.r.t time

put that velocity expression in (1) , you get acceleration w.r.t time

and dh/dt = v by this you will get h w.r.t. time

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