A tennis ball obeys the same quadratic-drag equation as the hailstone, (downward negative)

PHYSICS · Subjective · Fermi University Physics · Computational Physics · Mechanics & Dynamical Systems · Kinematics and Newtonian dynamics of particles

Computational Physics, Ch A falling body that knows about air: the first simulation

Problem

A tennis ball obeys the same quadratic-drag equation as the hailstone,

m\dot v = -mg + bv^2

(downward negative), and air resistance is the only force besides weight. It has mass

m = 0.058\,\mathrm{kg}

and drag constant

b = 0.020\,\mathrm{kg\,m^{-1}}

, and is released from rest at

y_0 = 25\,\mathrm{m}

above the ground. (a) Write the update rule

v_{n+1} = v_n + a(v_n)\Delta t

y_{n+1} = y_n + v_n\Delta t

with the acceleration

a(v)

given explicitly for this ball. (b) Hand-compute

v_1

and

y_1

after one step of

\Delta t = 0.10\,\mathrm{s}

, then

a_1

v_2

and

y_2

after a second step of the same size, using

g = 9.81\,\mathrm{m\,s^{-2}}

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